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    "# 08 - Instrumental Variables\n",
    "\n",
    "## Going Around Omitted Variable Bias\n",
    "\n",
    "One way to control for OVB is, well, adding the omitted variable into our model. However, that is not always possible, mostly because we simply don't have data on the omitted variables. For instance, let's go back to our model for effect of education on wage:\n",
    "\n",
    "$\n",
    "\\log(\\mathrm{wage})_i = \\beta_0 + \\kappa \\ \\mathrm{educ}_i + \\pmb{\\beta}\\mathrm{Ability}_i + u_i\n",
    "$\n",
    "\n",
    "To figure out the causal effect of education $\\kappa$ on $\\log\\mathrm{(wage)}$ we need to control for ability factors $\\mathrm{Ability}_i$. If we don't, we would likely have some bias, after all, ability is probably a confounder, causing both the treatment, education, and the outcome, earnings."
   ]
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   "execution_count": 1,
   "metadata": {
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     "hide-input"
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   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from scipy import stats\n",
    "from matplotlib import style\n",
    "import seaborn as sns\n",
    "from matplotlib import pyplot as plt\n",
    "import statsmodels.formula.api as smf\n",
    "import graphviz as gr\n",
    "from linearmodels.iv import IV2SLS\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "pd.set_option(\"display.max_columns\", 5)\n",
    "style.use(\"fivethirtyeight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "hide-input"
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    "g = gr.Digraph()\n",
    "\n",
    "g.edge(\"ability\", \"educ\")\n",
    "g.edge(\"ability\", \"wage\")\n",
    "g.edge(\"educ\", \"wage\")\n",
    "g"
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   "cell_type": "markdown",
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    "One way to avoid this is to control for constant levels of ability when measuring the effect of education on wage. We could do that by including ability in our linear regression model. However, we don't have good measurements of ability. The best we have are some very questionable proxies, like IQ.\n",
    "\n",
    "But all is not lost. Here is where Instrumental Variables enters the picture. The idea of IV is to find another variable that causes the treatment and it is only correlated with the outcome through the treatment. Another way of saying this is that this instrument $Z_i$ is uncorrelated with $Y_0$, but it is correlated with $T$. This is sometimes referred to as the exclusion restriction."
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   "cell_type": "code",
   "execution_count": 3,
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    "g = gr.Digraph()\n",
    "\n",
    "g.edge(\"ability\", \"educ\")\n",
    "g.edge(\"ability\", \"wage\")\n",
    "g.edge(\"educ\", \"wage\")\n",
    "g.edge(\"instrument\", \"educ\")\n",
    "g"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have such a variable, we can recover the causal effect $\\kappa$ with what we will see as the IV formula. To do so, let's think about the ideal equation we want to run. Using more general terms like $T$ for the treatment and $W$ for the confounders, here is what we want:\n",
    "\n",
    "$\n",
    "Y_i = \\beta_0 + \\kappa \\ T_i + \\pmb{\\beta}W_i + u_i\n",
    "$\n",
    "\n",
    "However, we don't have data on $W$, so all we can run is\n",
    "\n",
    "$\n",
    "Y_i = \\beta_0 + \\kappa\\ T_i + v_i\n",
    "$\n",
    "\n",
    "$\n",
    "v_i = \\pmb{\\beta}W_i + u_i\n",
    "$\n",
    "\n",
    "Since $W$ is a confounder, $\\mathrm{Cov}(T, v) \\neq 0$. We have a short, not long equation. In our example, this would be saying that ability is correlated with education. If this is the case, running the short regression would yield a biased estimator for $\\kappa$ due to omitted variables. \n",
    "\n",
    "Now, behold the magic of IV! Since the instrument Z is only correlated with the outcome through T, this implies that $\\mathrm{Cov}(Z,v) = 0$, otherwise there would be a second path from Z to Y through W. With this in mind, we can write\n",
    "\n",
    "$\n",
    "\\mathrm{Cov}(Z,Y) = \\mathrm{Cov}(Z,\\beta_0 + \\kappa\\ T_i + v_i) = \\kappa \\mathrm{Cov}(Z,T) + \\mathrm{Cov}(Z, v) = \\kappa \\mathrm{Cov}(Z,T)\n",
    "$\n",
    "\n",
    "Dividing each side by $V(Z_i)$ and rearranging the terms, we get\n",
    "\n",
    "$\n",
    "\\kappa = \\dfrac{\\mathrm{Cov}(Y_i, Z_i)/V(Z_i)}{\\mathrm{Cov}(T_i, Z_i)/V(Z_i)} = \\dfrac{\\text{Reduced Form}}{\\text{1st Stage}} \n",
    "$\n",
    "\n",
    "Notice that both the numerator and the denominator are regression coefficients (covariances divided by variances). The numerator is the result from the regression of Y on Z. In other words, it's the \"impact\" of Z on Y. Remember that this is not to say that Z causes Y, since we have a requirement that Z impacts Y only through T. Rather, it is only capturing how big is this effect of Z on Y through T. This numerator is so famous it has its own name: the reduced form coefficient.\n",
    "\n",
    "The denominator is also a regression coefficient. This time, it is the regression of T on Z. This regression captures what is the impact of Z on T and it is also so famous that it is called the 1st Stage coefficient. \n",
    "\n",
    "Another cool way to look at this equation is in terms of partial derivatives. We can show that the impact of T on Y is equal to the impact of Z on Y, scaled by the impact of Z on T:\n",
    "\n",
    "$\n",
    "\\kappa = \\dfrac{\\frac{\\partial y}{\\partial z}}{\\frac{\\partial T}{\\partial z}} = \\dfrac{\\partial y}{\\partial z} * \\dfrac{\\partial z}{\\partial T} =  \\dfrac{\\partial y}{\\partial T}\n",
    "$\n",
    "\n",
    "What this is showing to us is more subtle than most people appreciate. It is also cooler than most people appreciate. By writing IV like this, we are saying, \"look, it's hard to find the impact of T on Y due to confounders. But I can easily find the impact of Z on Y, since there is nothing that causes Z and Y (exclusion restriction). However, I'm interested in the impact of T on Y, not Z on Y. So, I'll estimate the easy effect of Z on Y and **scale it by the effect of Z on T**, to convert the effect to T units instead of Z units\". \n",
    "\n",
    "We can also see this in a simplified case where the instrument is a dummy variable. In this case, the IV estimator gets further simplified by the ratio between 2 differences in means.\n",
    "\n",
    "$\n",
    "\\kappa = \\dfrac{E[Y|Z=1]-E[Y|Z=0]}{E[T|Z=1]-E[T|Z=0]}\n",
    "$\n",
    "\n",
    "This ratio is sometimes referred to as the **Wald Estimator**. Again, we can tell the IV story where we want the effect of T on Y, which is hard to get. So we focus on the effect of Z on Y, which is easy. By definition, Z only affects Y through T, so we can now convert the impact of Z on Y to the impact of T on Y. We do so by scaling the effect of Z on Y by the effect of Z on T. \n",
    "\n",
    "## Quarter of Birth and the Effect of Education on Wage\n",
    "\n",
    "So far, we've been treating these instruments as some magical variable $Z$ which have the miraculous property of only affecting the outcome through the treatment. To be honest, good instruments are so hard to come by that we might as well consider them miracles. Let's just say it is not for the faint of heart. Rumor has it that the cool kids at Chicago School of Economics talk about how they come up with this or that instrument at the bar. \n",
    "\n",
    "![img](./data/img/iv/good-iv.png)\n",
    "\n",
    "Still, we do have some interesting examples of instruments to make things a little more concrete. We will again try to estimate the effect of education on wage. To do so, we will use the person's quarter of birth as the instrument Z.\n",
    "\n",
    "This idea takes advantage of US compulsory attendance law. Usually, they state that a kid must have turned 6 years by January 1 of the year they enter school. For this reason, kids that are born at the beginning of the year will enter school at an older age. Compulsory attendance law also requires students to be in school until they turn 16, at which point they are legally allowed to drop out. The result is that people born later in the year have, on average, more years of education than those born in the beginning of the year.\n",
    "\n",
    "![img](./data/img/iv/qob.png)\n",
    "\n",
    "If we accept that quarter of birth is independent of the ability factor, that is, it does not confound the impact of education on wage, we can use it as an instrument. In other words, we need to believe that quarter of birth has no impact on wage, other than through its impact on education. If you don't believe in astrology, this is a very compelling argument."
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    "g = gr.Digraph()\n",
    "\n",
    "g.edge(\"ability\", \"educ\")\n",
    "g.edge(\"ability\", \"wage\")\n",
    "g.edge(\"educ\", \"wage\")\n",
    "g.edge(\"qob\", \"educ\")\n",
    "g"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To perform this analysis, we can use data from three decennial census, the same data used by [Angrist and Krueger](https://economics.mit.edu/faculty/angrist/data1/data/angkru1991) in their article about IV. This dataset has information on log wages, our outcome variable, and years of schooling, our treatment variable. It also has data on quarter of birth, our instrument, and additional controls, such as year of birth and state of birth. "
   ]
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  {
   "cell_type": "code",
   "execution_count": 5,
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       "      <th>log_wage</th>\n",
       "      <th>years_of_schooling</th>\n",
       "      <th>year_of_birth</th>\n",
       "      <th>quarter_of_birth</th>\n",
       "      <th>state_of_birth</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.790019</td>\n",
       "      <td>12.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.952494</td>\n",
       "      <td>11.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.315949</td>\n",
       "      <td>12.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.595926</td>\n",
       "      <td>12.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>45.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.068915</td>\n",
       "      <td>12.0</td>\n",
       "      <td>30.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   log_wage  years_of_schooling  year_of_birth  quarter_of_birth  \\\n",
       "0  5.790019                12.0           30.0               1.0   \n",
       "1  5.952494                11.0           30.0               1.0   \n",
       "2  5.315949                12.0           30.0               1.0   \n",
       "3  5.595926                12.0           30.0               1.0   \n",
       "4  6.068915                12.0           30.0               1.0   \n",
       "\n",
       "   state_of_birth  \n",
       "0            45.0  \n",
       "1            45.0  \n",
       "2            45.0  \n",
       "3            45.0  \n",
       "4            37.0  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"./data/ak91.csv\")\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The 1st Stage\n",
    "\n",
    "Before we use quarter of birth as an instrument, we need to make sure it is a valid one. This implies arguing in favor of the two Instrumental Variables assumptions:\n",
    "\n",
    "1. $\\mathrm{Cov}(Z, T) \\neq 0$. This is saying that we should have a strong 1st stage, or that the instrument indeed impacts the treatment variable.\n",
    "2. $Y \\perp Z | T $. This is the exclusion restriction, stating that the instrument Z only affects the outcome Y through the treatment T. \n",
    "\n",
    "The first assumption is fortunately verifiable. We can see from data that $\\mathrm{Cov}(Z, T)$ is not zero. In our example, if quarter of birth is indeed an instrument like we've said, we should expect individuals born in the last quarter of the year to have slightly more time of education than those born in the beginning of the year. Before running any statistical test to verify this, let's just plot our data and see it with our own eyes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "group_data = (data\n",
    "              .groupby([\"year_of_birth\", \"quarter_of_birth\"])\n",
    "              [[\"log_wage\", \"years_of_schooling\"]]\n",
    "              .mean()\n",
    "              .reset_index()\n",
    "              .assign(time_of_birth = lambda d: d[\"year_of_birth\"] + (d[\"quarter_of_birth\"])/4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0XgjRYLp3785zzz3HmTNnWL16NVdddRUTJ07EZrMxd+5cwsPDmTlzpiOJB1Aqlbz00ksoFArHj+NSVc2HViqVTJo0CYC1a9dWGcf48eMrJfGl1Gp1lb2FFX9UVad0uPOMGTOchjHrdDpH73JdhunXZu/evbz++utV/vfDDz849tu2bRupqan07du3UsJ6zz33EBsbWy/xfPzxx1gsFp566qlKSTxATEyM0+Oq3kNvb28mTpyI1Wplw4YNFxzThbwnr7/+uiOJh5KaD9dccw15eXmkpqbWKY5JkyY5kngo6Qkv/Wx/+eWXjvbIyEiuvfZadu3axZ9//ul0jk8//RSAu+++u9brlQ6PraonuiJfX19CQkIA6jxMuqK2bdtWSuIBx5Di6r6X11xzTZVJfG3mzp2L3W7n7bffrjSEeOzYsXTr1o1Vq1Y5TWEo9cgjj7icxENJkmMymbjnnnuckniAp556iqioKH7++WfHvPj6UP47/cEHH7BlyxY6dOjADTfcUOeCY88995zLf8uqcv/991f6Xo8bNw6AHTt2uHSO0pt57ihYV9PzK/89LqVQKByf+/pQ1TU0Gk2d3iedTlflc4iOjmb06NGkpqY6huoDfPPNN1gsFiZOnOg0mkKhUPDiiy86/Xta6kK+M6XvW8WbskKIhic98kKIBvXwww/zwQcfcPbsWcd8+cOHD5OVlcUll1zCG2+8UeVxPj4+HDp0yKktOzub9957j9WrV3P8+HEKCwudtlf3Y/rSSy+tsv3mm2/mo48+ok+fPlx//fVcfvnl9O3b1+Xhg/n5+Rw9epQWLVpU+pEPMHjwYAB27drl0vlccdttt7m0HFDpNQcMGFBpm1KppF+/fhw9evSC4/njjz8AXE7ITp48ybvvvsv69es5depUpTnUF5oQXch7EhgYWOUNjtKbEXVdKrGq1z4+Pp4WLVpw9OhR8vPzCQgIAEpurixdupRPP/3UMXz68OHDbNy4kX79+tG5c+c6XbsuLnSd6MLCQscw8yNHjpCfn+9UU6Cu38vabNu2DS8vL1asWMGKFSsqbTeZTFitVo4cOUKPHj0u6Jqln5OqpqJotVr69evH999/z+7du4mKiqrTuatT/nNWWFhISkoK06ZN49577yUlJaXK5duqc76vcamKrx/U/fuQnZ0N4JYVSqp6fh07diQhIYFvv/2WEydOcM0119C3b1969eqFVqutl+teffXVvPLKK0yZMoVffvmFK664gt69e9OlSxeUyrr3mW3dupW5c+eSnJxMZmZmpRoxaWlpjpuCu3fvBuDyyy+vdJ7SegAnTpxwar+Q70zpv4eujlITQriPJPJCiAalVCodvaKlP6JKf9j9/fffvP766y6dJzc3l6FDh3L8+HEuvfRSxo4dS3BwMCqVCr1ez9y5c6tNSKobNjxz5kxiY2P56quveO+993j33XdRKpUMHjyYl19+udZ5mnl5eTWe39fXl8DAQPR6vUvPsT6VxhYeHl7l9gsZSl1e6XNr2bJlrfseO3aMYcOGkZuby+WXX87QoUMJDAxEpVI55hVfaFJ5Ie9JdXUKSnu4qiqoWJPqYggPD+fs2bNOifygQYPo2LEj3333HTNmzCAwMLBOvfFQ1nN2+vTpWvctKipyfA+r+4y4wmw2M3r0aHbs2EHnzp0ZM2YMYWFhjlEur7/+ep2/l7XJzs7GYrHU+rejquKBdb1mbZ+n0tfcXd9xPz8/Lr30Ur744gu6dOnCu+++y913311ppEt1LrQXvKrvRF2/D6V/9y/0u12Vqp6fSqVixYoVvPHGGyxfvpyXXnoJKPnujxkzhpdffvmCRilAScK8du1aXn/9dX755RfHaKgWLVpw33338fjjj1fZM16VFStWMH78eLRaLUOGDOGSSy7B19cXpVLJpk2b2Lx5s9Nr58rf9oqJ/IV8Z0pvtlY1+kAI0bAkkRdCeFxpMZ4RI0awePFil4754osvOH78OFOnTq00z3D79u3MnTu32mOrGvYLJT/4Jk2axKRJk8jOzmbr1q0sX76c//3vf4wZM4bt27fXOAyz9HlkZGRUub2oqIi8vLx6HcrpqtLYMjMzq9xeVcylPUnV/UCvKfk9c+ZMrT1us2fPJjs7m9mzZ3PHHXc4bVuyZEmlyvXnozG9JxkZGcTHx1dqL31PSpP4UhMmTODpp5/mf//7H+PGjWPRokWEhIRw/fXXu3S9nj17otVqSUtLIyUlpcZ58ps2bcJqtRIUFETbtm0d7Uql0jG/t6Kq3v9Vq1axY8cObr/9dj744AOnbenp6TUmDtV9L2sTGBiI2Wx2Gm7sqrpes7bPU+l0huoKjNWXoKAg4uLi2LVrF7t27XI5kT/f17g+lSacpTeO6lN1zy8oKIgZM2YwY8YMjh07xu+//86XX37JwoULOXHiRJW90nXVvn17Pv74Y6xWK/v27WPDhg3Mnz+f6dOnY7VanQp01uTVV1/F29ubdevW0aFDB6dtjz32GJs3b3ZqK/27UZe/7RfynSl938LCwup8rBCifskceSGEx7Vv3x6dTseff/5Z5TJzVSkdBl5x+SKg0g+d8xESEsI111zD3LlzufHGGzl37hxbtmyp8ZiAgABiY2PJyMggJSWl0vbS+d5VDU91t/LLKlVks9nYunVrpfbSRLyquZAWi8UxpLO8yy67DIBffvml1pjO5z2sa+9fY3pPqnpOpcXlYmNjKyXyY8eOxd/fn08//ZRly5aRnZ3N7bff7lJlcCjpMbvlllsA+M9//lPtfjabjTfffBOAG2+80WkocFBQEBkZGVUm8zt37qzUVvqeli4ZV975fi9re8979+5Nfn4+e/bsOa/z10Xp96h0qbDyjEajY3mw0v3cqXQou81mu+BzlS8u6m6lc+wrTpVqKG3btuX2229n+fLlxMTEsHHjRsdNqfp4HVQqFd26deOhhx5iyZIlQMlSqeW3Q/Wf56NHj9KhQ4dKSXx1f6dL671U9e/TiRMnqhyRcyHfmdLaIK6uJCCEcB9J5IUQHufl5cWkSZPIyMjgqaeeoqioqNI+WVlZToljaVGfTZs2Oe23a9cu3n777TrHYDQaq/whZLfbHT0dvr6+tZ7nrrvuAkoqopdPfvLy8hw1AUqLQzWkvn37Eh8fz7Zt21i2bJnTto8//rjK+fEBAQF06NCBbdu2sW/fPke73W7ntddeqzLBv+eee/Dy8uLNN99k//79lbaX/1FZ3Xv466+/VrtGemnPeV16khrLezJ37lynuK1WKy+++CJ2u73SiAQo6TW7+eab2b9/P9OmTUOhULg8rL7U888/T8uWLfnuu++YNm1apYS8sLCQyZMns337diIjIyutXnDZZZdhsVgqFQP89ddfq6yGXd17euzYMV588cU6xV6q9D2vrrhWaRG9xx57rMqkpbi4uNabcK665ZZb8Pb25uOPP66UiP73v//lzJkzJCUl1dv8+OqsXLmS48ePo1ar6du37wWf73y+V+erU6dOhIWFuVwc70IdO3aMY8eOVWovKCigsLDQqcBpUFAQCoWizoXc/vrrryprBJSO0Cj/b0dtn+fWrVtz9OhRp1oSdrudmTNnVnkz8uabb8bLy4v58+c7DaG32+28/PLLVd4wuJDvTHJyMkFBQZLIC9EIyNB6IUSjMGXKFPbv38+CBQtYvXo1iYmJREdHc+7cOf7++2+2bt3KxIkTHb0PY8eO5b333nMs79SuXTuOHDnCzz//zKhRo/juu+/qdH2DwcDVV19N27Zt6dmzJ61atcJsNrNp0yb27NlD7969XVoa7sEHH+SXX37hl19+oX///lx11VWYzWZWrFjBmTNnGDt2rMtDo11R0/JzAI8//jharRaFQsGsWbMYM2YMd999t9M68uvWrePKK6+sshf90UcfZfLkyVx99dVcf/31+Pr6sm3bNk6fPs3AgQMrJWwdO3bkrbfe4vHHH2fIkCGOdeRzcnLYvXs3RqPR0Zt5zz33sHDhQv71r3851uM+cOAAv/zyC2PGjKnyPRw6dCh//vknd911F0lJSWi1Wlq1asXYsWOrfQ0a+j2pTp8+fRg0aJDTOvL79++nV69e1S4jds899/Dpp59y5swZBg8eTLt27ep0zRYtWvD9998zduxY3nnnHZYsWcIVV1xBWFgYaWlprFmzhszMTAIDA1m0aBGRkZFOx99///0sXLiQKVOmOJZpO3jwIGvXrmXUqFGVbgqNGDGC2NhYZs+ezf79++nWrRunTp3i559/Jikp6bwqXcfHxxMTE8OWLVu49957adeuHSqViquvvpquXbuSmJjIK6+8wosvvsill17K8OHDadu2LcXFxZw8eZLff/+d1q1bV/qsno/WrVvz+uuv88QTTzB06FCuv/56IiIi2LZtG5s3byY6Opq33nrrgq9TXvnvd1FREQcPHmTNmjVAyRKG9VHfYujQobz33nu8/PLLHDhwwDEap76WpSxPoVAwcuRIPvvsM/bs2eP2hHDv3r3cdddd9OjRgw4dOhAVFUVubi4///wzOTk5PPTQQ46lHP39/enTpw/btm3j1ltvpXv37qjVavr3719lscpSixcv5tNPP6Vv377ExsYSEhLCyZMnWbVqFSqVikceecSxb58+ffDz8+O7775DrVbTqlUrFAoFt956K61bt2by5Mk8/vjjJCYmMnr0aLy8vNi2bRsHDx5kxIgR/PTTT07XvuSSS/i///s/Xn75ZQYNGsQNN9zgWEc+JyeHrl27Ot2IBc77O3Po0CFOnTrFnXfeeV5F/IQQ9UsSeSFEo+Dl5cWCBQv49ttvWbhwIWvWrKGgoICQkBBatWrFE088wa233urYPyoqih9//JFp06axdetW1q5dS3x8PG+99RaDBw+ucyLv5+fHyy+/zMaNG0lOTubHH3/Ex8eHNm3aMH36dO6+++4ql6WryNvbm++++445c+bw9ddfM3/+fJRKJZ06deKZZ55x9A7Xl71797J3795qtz/wwAOO4lL9+vXjxx9/5JVXXuHXX3/l119/5dJLL2XlypX8+uuvVSbyt99+OwDvv/8+ixcvxt/fn2HDhvHFF18wY8aMKq85fvx4OnfuzKxZs9i6dSs//vgjISEhdOjQgYkTJzr269q1KytWrGD69On8/PPPWK1WunbtyhdffIFOp6vyPXzyySfJy8vjxx9/5N1338VisTBgwIAaE/mGfk+q89prr7F8+XIWLFjAiRMnCAsLY/LkyTz77LPVDpfv2rUrPXv2ZOfOnUyYMOG8rtuhQwd+//13Pv/8c5YvX87y5cvJzc11VJK/5ppreOedd6pMCNu3b8/y5ct55ZVX+OWXX1AqlfTs2ZPly5fz999/V0rk/fz8HAXFNm3axJYtW2jbti1TpkzhwQcfrPP3EkqGIn/55ZdMmzaNn3/+2VEFv2XLlnTt2hUoWQ2jX79+zJ07ly1btvDTTz/h7+9PVFQUt9xyi0vrm7vq7rvvJjY2llmzZvHDDz9QWFhIVFQU9913H0899VS9FY4sVb6ugEqlIiwsjBEjRnDfffcxdOjQernG0KFDee211/jss8+YP3++o5iaOxJ5KFl7/rPPPmPRokVuT+R79uzJE088waZNmxzJbUhICO3bt+fVV1+tdBPvww8/5LnnnmPLli2sWbMGm83G1KlTa0zkb7rpJsxmM9u2bWPPnj0UFRURGRnJiBEjmDx5slM1/aCgIL788ktef/11vv/+e0dBuX79+tG6dWvuvvtuvL29mTNnDosWLUKr1XL55Zcze/Zsli9fXimRB3jiiSdo2bIls2fP5quvvsLf358rrriCl156iRtuuKHStB04v+9Mad2S8n/HhRCeo8jNzbXXvpsQQgghGlpRURGdOnVCq9Wyd+9e1Gp1vZ37hx9+4K677qJDhw6sXLnygit3C1EXN954I3/99Re7d+929IiL+pWXl0f79u1JSEhwjOI4X8XFxfTo0YO4uDinOf9CCM+RcTFCCCFEI/XZZ5+h1+u5++676zWJB7j22muZMWMGBw4c4Prrr3d5HXAh6sP06dPJzc2tcYUR4ZqsrKxK9S8sFgvPP/88xcXFjBw58oKvMW/ePDIyMnj11Vcv+FxCiPohQ+uFEEKIRkSv1/PJJ5+QlpbGggULCAsLY9KkSW651gMPPICfnx+nT59my5YtXH311W65jhAVderUiQ8++MAty9BdbH744QdefvllhgwZQnR0NDk5Ofz+++8cPnyYhIQE7rvvvgu+hlarZdasWY46NUIIz5Oh9UIIIUQjcvz4cbp3745GoyEhIYHXXnvNsayfEEJUtGfPHv7zn/+wY8cOx42RNm3aMGrUKB599NEq58gLIZo+SeSFEEIIIYQQQogmRObICyGEEEIIIYQQTYgk8kIIIYQQQgghRBMiibwbpKamejoEIc6LfHZFUyWfXdFUyWdXNFXy2RVNWXP4/EoiL4QQQgghhBBCNCGSyAshhBBCCCGEEE2IJPJCCCGEEEIIIUQTIom8EEIIIYQQQgjRhEgiL4QQQgghhBBCNCGSyAshhBBCCCGEEE2Il6cDEEIIIYQQQggh6tOGDRvQ6/VVbjMYDKSkpFS5TafTkZiY6M7Q6oUk8kIIIYQQQgghmhW9Xk96enqN25sySeSFEEIIIYQQQlw0NBoNo0ePRq1Ws27dOtLS0jwdUp3JHHkhhBBCCCGEEBeNpKQkYmJiaNmyJQEBAZ4O57xIIi+EEEIIIYQQ4qIQFxdHmzZtMJlMng7lgkgiL4QQQgghhBCi2VOr1QwcOBC9Xs/x48c9Hc4FkUReCCGEEEIIIUSzN3z4cPz8/Fi7di12u93T4VwQSeSFEEIIIYQQQjRrbdu2JTY2liNHjnD69GlPh3PBJJEXQgghhBBCCNFsKRQKEhMTHevHR0dH4+PjA0BISAhBQUGeDfA8yPJzQgghhBBCCCGaLbVaja+vL35+ftxwww1ASXIP0L9/f9q1a8fChQs9GWKdSSIvhBBCCCGEEKLZMpvNJCcn4+VVlv7Gx8cTGRnJwYMHSUlJ8WB050cSeSGEEEIIIYQQzZbdbmfHjh1ObWFhYURGRpKamsqRI0c8FNn5k0ReCCGEEEIIIcRFJSMjA51OR35+vqdDOS+SyAshhBBCCCGEuKgkJyeTnJzs6TDOmyTyQgghhBBCCCGaFZ1Ox95sM3qTzdEWrlXRPsgLg8HgqFpf1XFNgSTyQgghhBBCCCGalcDO/Xj9SKZTxvvb1eH0CPMmNTWV+Ph4zwVXD2QdeSGEEEIIIYQQzcr7+wqcHg+K9KZHmLeHoql/ksgLIYQQQgghhGg2ThRY+P5vg1Pbw10DPBSNe0giL4QQQgghhBCi2Zi7vwCrvexxxyAvrozReC4gN5BEXgghhBBCCCFEs5BrtLHgYJFT2+Qu/igVCg9F5B6SyAshhBBCCCGEaBYWHCqkwFLWHd/CR8ktsb4ejMg9JJEXQgghhBBCCNHkmax25u53LnJ3Xyd/tF7NqzceJJEXQgghhBBCCNEMfPe3gTNFZevG+3opmNCh+fXGgyTyQgghhBBCCCGaOLvdzqy9+U5td8T7EqJVeSgi95JEXgghhBBCCCFEk/bbGSP7ciyOxwpgcmd/zwXkZpLICyGEEEIIIYRo0t7f5zw3flQbLZcEenkoGveTRF4IIYQQQgghRJO1N9vMr6eNTm0Pdw3wUDQNQxJ5IYQQQgghhBBN1uwKvfH9WnjTu4W3h6JpGJLICyGEEEIIIYRoks4UWllytMip7aGuzXdufClJ5IUQQgghhBBCNEkfHSjAXLbiHLEBKq5upfVcQA1EEnkhhBBCCCGEEE1OvtnGpwcLndoe7OqPSqnwUEQNRxJ5IYQQQgghhBBNzpeHitCb7I7HIRolt8X5ejCihiOJvBBCCCGEEEKIJsVis/PBfucidxM7+eHrdXGkuM13YT0hhBBCCCGEaKQ2bNiAXq+v83E6nY7ExEQ3RNS0LD9m4GSB1fFYo4J7O/p5MKKGJYm8EEIIIYQQQjQwvV5Penq6p8Nokux2O7MqLDk3tp0v4T4qD0XU8CSRF0IIIYQQQohGRKPRMHr0aNRqNevWrSMtLc3TITUqv581sfOc2antwS7Nf8m58i6OCQRCCCGEEEII0UQkJSURExNDy5YtCQgI8HQ4jc6svc698SNaaWkfpPZQNJ4hibwQQgghhBBCNBJxcXG0adMGk8nk6VAapUO5Zn46WezU9nDXi6s3HiSRF0IIIYQQQohGQa1WM3DgQPR6PcePH/d0OI3S7Apz43uGqekf4e2haDxHEnkhhBBCCCGEaASGDx+On58fa9euxW63137ARSbDYGXxkSKntoe7+KNQKDwUkedIsTshhBBCCCGE8LC2bdsSGxvL4cOHOX36ND169PB0SE6MB97BVnS6zscpfaPRdHqsXmKYn1KIsWzFOVr5qxjd1qdezt3USCIvhBBCCCGEEB6kUChITEzEYDCQkpJCdHQ0Pj4lCWpISAhBQUHk5uYCcDTPwokCC639GzaVsxWdxqbf06DXLK/IYmP+gUKntsmd/fFSXny98SCJvBBCCCGEEKIZaAw9xnWRabA5/l+tVuPr64ufnx833HADgGO4eP/+/WnXrh0LFy4EIK3ISq8lZ7kp1ofHugXQ0VPV2hUqtDHD8YlKRKkOwG4txpj5B4VHvgFstR5eV4sOF5FtLDuvzlvBne196/06TYUk8kIIIYQQQogmz9M9xq4qtth5ZlsuWr2Zdv+0mc1mkpOT8fIqS8/i4+OJjIzk4MGDpKSkOJ3DYofFRwwsPmLg2tZaHu8WwGXhJQXfNJ+8gTL9VJ3jskXGYJwwxeX9tS2HENzreWymHGxGPQq1H5oWfdGE9yZ761N1vn5NrDY7syssOXd3Bz8C1BdvyTdJ5IUQQgghhBDNTwP3GLviaJ6F8euy2ZNtZlK5drvdzo4dO5z2DQsLIzIyktTUVI4cOVLtOX84UcwPJ4oZFOnNE90CuDr9FKqDu9z0DMpYDZkUHV9B/oH52IxZKL11hA54D+/QBLwCYrHkH623a606WczR/LLJ8Wol3Nfp4ltyrjxJ5IUQQgghhBDNTkP2GLti2TEDD23KId/sWjX6jIwMdDod+fn5Tu0+qqrnhG9MN7ExPYttWSYurbhxYBKKXgNQhLQAH19sc6bDsVSX4jDb7KTqLfgXWwkt3569G332bsdjm0mPpfAk6qD2qPyi6zWRr9gbf1OsLy39VPV2/qZIEnkhhBBCCCFEs9OQPcY1MVrt/DtZz0cVCrXVJjk5meTk5ErtPcO9+TwhhLd35/NXlrnS9oIqbhQoJzwJ/jooLkIRGAzB4VUm8pkGK3uzzezNMbMv28y+HAsHc82YbPBNhIX+2urjVah88PJvi6UoHXP23jo915pszzCyNcPk1PZQl4u7Nx4kkRdCCCGEEEI0Qw3ZY1yd4/kW7v4tmz/PVU64/QJ0hPtqqKaDvVo6nY7Etj6MbqPltzNG3t5TwIY0Y43H2Jd9if3QHhTXjUPRb2iV+2zLMJG4OL1uwZRSqAjuOxMv/1YU/v0dNlOOY9OpQivBxVbCtOfXg/5+hd74K6I1dAnxUIG/RsSjifzmzZuZNWsWu3btIi0tjdmzZ3PHHXc4tk+fPp1ly5Zx+vRp1Go13bt357nnnqNv3741nnfTpk0899xzpKSkEBkZyaOPPsqECRPc/XSEEEIIIYQQjZS7eoyrs+qEgQc25qA3OfeQq5Xwah8dEzte6ahMfz4UCgVDo7UMjdbyR6aJt3fn88OJ4ir3tS/7ouR/rh1b7fnMNteG/FemJLjPDDRhvShO30jenvecth4rsDDw63TGtPXh3k7+XPpPUT5X/J1nYcVx5+ckvfElPJrIFxYW0rlzZ2677TYmTZpUaXt8fDxvvvkmbdq0wWAw8MEHH3DTTTexY8cOWrRoUeU5jx07xi233MIdd9zBRx99xNatW3nyyScJDQ3luuuuc/dTEkIIIYQQQjQ2NfQY78o2sXt/ATfG+hB6nr3G5Zltdl7ekcesCj3JAK39VXw2JIRedUhmXXFZuDcLrwjlYK4Z3xQV6Ov19LT0VRKiqapCvJLgPtPRRvSnOGMrOdv/DVS+IWC0llXZ7xWmZmJHP264xBetl4Klmz8hK6/qkQBH8yxcT1mROz8vBUd2e3N0N4QGRnL9gIu3s9ajiXxSUhJJSUkATJ48udL2W2+91enxjBkz+OKLL9izZw9XXHFFlef89NNPiYyM5I033gCgQ4cO/PHHH7z//vuSyAshhBBCCHHRqbnHON9s5+ltev5vu56kVlrGtvPlqlZaNP+Mea8p0azIaLVzMNdCntnGUMJZxxjHtqtbaZkzKJigKhPi+tEhSI2PzgvOc4S8VgUdg9R0DVHTJVhNlxA1XYO9CNGqMOxQY3O6QaAguPcraCMHYsxMJmfbs7iyGsCf58xM3pTL88l5jGvvS3hOGunnDlW5rxKIKT9owQrHz57fc2tumswceZPJxOeff05gYCAJCQnV7rd9+3aGDRvm1HbFFVewaNEizGYzarXMpxBCCCGEEOLi4FqPMZSszb7qRDGrThQT5K3ghkt8GRvnw7m8dI6fPejyFQOBQEXZZbwU8OJlgTzUxf+ChtK7W68wb07d2RIvpWsx+rYZhTZqEDZLESqfcMKHfFKyQaki/8AnFJ9ZC4C2miIA2UYb7+wp4AZMRJfbRaX04pp+txMVGoO3WovJYuLI6X38tnMFVpvlgp5jc9LoE/mffvqJe+65h6KiIiIjI/n++++rHVYPJcs0DBkyxKktPDwci8VCVlYWkZGRVR6Xmura8guuqu/zCdFQ5LMrmir57IqmSj67oqlqbJ/dUIMBjVOLaz3GlwbaSI4vquKMhaAHg8Hg1OpqotlLZ+P/EkrPW8Thwxf4BF0UZzAQcD4Hmov5+0j1QVZ8fa3Gc5hy9oPd6ryjQoXdUvZ6dvGzkjywqte3xE97bGTklT3W+YfQP2E4RYZ8jOZiQgJ96dS6J3HRXfhw+XTHfkUGwwV9Bhvb57ei+Pj4Grc3+kR+0KBBbNy4kaysLD7//HP+9a9/sWbNmmoT8vNV2wtVF6mpqfV6PiEainx2RVMln13RVMlnVzRVjfGzeypT45RoutpjnGXz5o49gRzSV93bOwal0/BuVxPNvw1ehLSKrZd593Xh4+NzXsf5+vjU+J4a8nywlVsFzpj+O8b0312Kp/S8R/MsfJxSyJephY4igBVf37zCbD5cNp0TZ1Ox2W1o1FoeunE6rSLiCPQLJq8wx6V4a9IYP7911egTeT8/P2JjY4mNjaV379706tWLBQsW8PTTT1e5f4sWLcjMzHRqy8zMxMvLi9DQ0IYIWQghhBBCCNGAdmeZOKc307dcJu9qj3GMn4ptg1qw85yZRUeK+PaogWxj9XO9XU00O4eoGzyJr47yuXchPBJ8Siq+K+9+AsY/in3zGuzfzHftHL7R53ftcsfFBnoxo4+O53oFsOSogXkHCiHbeX+L1cKx9LKpDEZzMUZTEQoUqJSNPn1tME3ulbDZbJhMpmq39+nTh5UrVzq1rVu3jp49e8r8eCGEEEIIIZqZs0VWbv81m7crrErmao8xlCzl1ivcm17h3szoreOX08UsPlzETyeLK43GdzXRbEyz4e15OSh8fKEgD3vmmXLtuS6fQ9PpsXqLx9dLybj2ftwV78s7y9Vk51TeZ+TldxAV2gY/nwCiQluTcuIvcvIzK+94kfJoIl9QUMDRo0eBkgT91KlT7N69m+DgYHQ6He+99x4jRowgIiKCrKws5s2bx5kzZ7j++usd57j//vsB+PDDDwG4++67mTdvHs888wx3330327Zt46uvvmL+fNfuNAkhhBBCCCFgw4YN6PVVr2NmMBhISUmpcptOpyMxMdGdoTkUW+zcsTaLU4VWjmrKpt7GBXgR6etab3jFnmZvlYJrWvtwTWsfcow2Zq/0wphf+bimlGjaZ02rpsSfZykUCgK9lRU75QFoFRFHqC4CrdoHi9WMvqCqvS5eHk3kd+7cyahRoxyPZ86cycyZM7ntttt46623OHDgAF9++SXZ2dmEhITQs2dPVq1aRdeuXR3HnDp1yumcbdu25euvv+b//u//+OSTT4iMjOT111+XpeeEEEIIIYSoA71eT3p69euYVZfkNxS73c7Dm3P4I9MMwNTs8QDc38mP4f2C6uUawRolUb4qjlWRyDfWRNMWGdOgx7nLnKUvARDkH8rEkc/Qp/MwdqZu4u8011cQaM48msgPGjSI3NzcarcvXLiw1nP88MMPldoGDhzIhg0bLiQ0IYQQQgghRDU0Gg2jR49GrVazbt060tLSGjyG/+4u4JujzhXlr4jWMKOPrkGu31gTTeOEKR69fn3LLcgi5cQukiLiiY/p5vHXt7FocnPkhRBCCCGEEM6Wbv6ErLzqe8+rExoYyfUDJtT5uKSkJGJiYlCpVAQEBDR4Ir/8mIFX/sxzamuv8+LjwSEur4NeXyTRrF+tW8ThpfLiaFrJ1A1fjT/xMV0pNhmcahNc7CSRF0IIIYQQoonLykvn2NmGSXLi4uJo06YNJpPpvJc6uxC7skxM2uhcHS1Yo2DxlaEEaZRuv74kmu6VENuHIT1HkVOQhcVqxlfjT4BfEEdO7+PQyd2eDq/RkEReCCGEEEKIZkal9OKafrcTFRqDt1qLyWLiyOl9/LZzBVZb1eull7LY7BzPt1a5BJtarWbgwIHo9XpycnLo2LGju55CldKLrNz+SzZFlrLSbV4KWDA0lNjAhkltJNF0r027f8JH60eYLgqVyovsvLPsT97Jln1rPB1aoyKJvBBCCCGEEM2Mzj+E/gnDKTLkYzQXExLoS6fWPYmL7sKHy6c79ssz2fgytZDDegupeguH9RaO5lsw22CSxUy7CucdPnw4fn5+LF26lB49ejToczJY7Nzxaxani5zXhX/r8iAGRWmqOar+SaLpXvqibJb8Ns/TYTR6ksgLIYQQQgjRzOQVZvPhsumcOJuKzW5Do9by0I3TaRURR6BfMHmFJUPTd2eb+X5TrkvnbNu2LbGxsRw+fJjTp083aCJvt9t5aFMOO86Zndof6OzH+A5+DRYHSKJZ30IDI2vfqR6Pay4kkRdCCCGEEKKZsVgtTvO1jeZijKYiFChQKeueAigUChITEx3rx0dHRzvmx4eEhBAUFORYjWp/jpn4XDMdg9T18lwA3tyVz7d/O1eovzJawyu93V+hXhJN9zqfYotCEnkhhBBCCCGarZGX30FUaBv8fAKICm1Nyom/yMnPrPW4Fj5KAo1KMJU8VqvV+Pr64ufnxw033ACUJPcA/fv3p127do6lo3OMNgYszeDuDn480zOAMK3qgp7DsmMGZux0Xsi9g86Lj4c0TIV6STRFYySJvBBCCCGEEM1Uq4g4QnURaNU+WKxm9AXZTtv9vBSMjtYSr/MiTqemvc6LdoFeBGmUrFihJv2fFe3MZjPJycl4eZWlD/Hx8URGRnLw4EFSUlKczmu1w/yUQr4+UsST3QO4v5M/Wq+6J91/nTMxaYNzhfoQjZLFV4ai83Z/hXohGitJ5IUQQgghhGim5ix9CYAg/1AmjnyGPp2HsTN1k2Ot855h3twzLLTW89jtdnbs2OHUFhYWRmRkJKmpqRw5cqTK4/LMdl78I4+PUwqZdmkgYy7xcfTk1yatyMrtv2ZhsFaoUD8shEsaqEK9EI2VfAOEEEIIIYRo5nILskg5sYukiHjiY7o5EvkLkZGRgU6nIz/fedi7VlU5UT9RYGXC+hzm7i9kyYlPiMg9U+O5rXbIyzbxhbksiT/kE4X5nqcYGNlwFeqFaKwkkRdCCCGEEKKZad0iDi+VF0fTSoa8+2r8iY/pSrHJ4FQE70IkJyeTnJxcqb1nmDfTYwN5Y1c+epPdadv2TBOpKX/TUp9S6bjyVMClFdpa+qmIat+wFeqFaKwkkRdCCCGEEKKZSYjtw5Ceo8gpyMJiNeOr8SfAL4gjp/dx6ORul86h01VfEd5gMDiq1ld13HVdA7g9zpfX/8rn45RCLPYqdy0zMAlFrwEoQlqAjy+2OdPhWKrTLpcEeFHsUuRCNH+SyAshhBBCCNHMbNr9Ez5aP8J0UahUXmTnnWV/8k627Fvj8jkSExOr3Zaamkp8fHyNx4doVbzeL4h7O/nxwh95rDpRfRqunPAk+OuguAhFYDAEh1dK5N1fn16IpkMSeSGEEEII0WRt2LABvV5f5+N0Ol2NiWpTU7HDW1+UzZLf5nkkloridGq+uiKUjWlGntte9XtlX/Yl9kN7UFw3DkW/oQ0coRBNjyTyQgghhBCiydLr9aSXrpF2ETN6hXPKbnRq6xnqjZ+65n7s0MBId4blZFCUht9Gh1PwhxdUyOfty74o+Z9rxzZYPEI0ZZLICyGEEEKIZkmj0TB69GjUajXr1q0jLS3N0yG5hd1uZ4XperZicrRd21rLI1fUvqxcQ1MqFET4qDwdhhBNntLTAQghhBBCCOEOSUlJxMTE0LJlSwICAjwdjttsTDexNcPk1Dale/N9vkIISeSFEEIIIUQzFBcXR5s2bTCZTLXv3MS98Vee0+Ph0Rp6hHl7KBohREOQRF4IIYQQQjQrarWagQMHotfrOX78uKfDcautZ41sTK/QG99DeuOFaO4kkRdCCCGEEM3K8OHD8fPzY+3atdjttS1g3rS9uSvf6fHgKA19Wmg8FI0QoqFIIi+EEEIIIZqNtm3bEhsby5EjRzh9+rSnw3GrPzNN/HLauVL9U010brzyuXdRvvM/FPEJJY/vfqLk8c0TPRyZEI2TVK0XQgghhBBNlq1ch7tCoSAxMRGDwUBKSgrR0dH4+PgAEBISQlBQELm5uZ4J1A3eqNAbf3mENwMjm+bceHteDgofXyjIw555plx7rueCEqIRk0ReCCGEEEI0Sal6M7uzzJSuhK5Wq/H19cXPz48bbrgBKEnuAfr370+7du1YuHChh6KtX3uyzfx4stipbUr3AMfzbWrss6bRvCdBCFG/JJEXQgghhBBNit1uZ+HhIp7eqmecxeZoN5vNJCcn4+VV9hM3Pj6eyMhIDh48SEpKiifCdYu3KvTGXxqmZmjLpjE33hYZ06DHCdEcSSIvhBBCCCGaDL3JxhO/5/Lt34ZK2+x2Ozt27HBqCwsLIzIyktTUVI4cOdJQYbrVwVwzy445P/8pPZpOb7xxwhRPhyBEkyeJvBBCCCGEaBK2ZxiZuD6HEwVWl4/JyMhAp9ORn59f+85NxFu78p2GoSeEqLkqRuuxeIQQDU8SeSGEEEII0ahZbXbe2VPAqzvzsFaYSK1UKKhpcnVycjLJycnuDbABHdFbWFJhNMJTTXhuvBDi/EgiL4QQQgghGq0zhVbu35DNxnRTpW1dQ9Rc7hcKhuortVvtJcu0mcqVtw/yVtJBp3NLvO723z35TpX6OwV5MaqN9MYLcbGRRF4IIYQQQjRKP54w8OCmXLKNtkrb7u/kx0uX6dB6Dan1PPa/i7j7t5yyBht81iqkHiNtGMfzLfzvcJFT25PdA0pGJQghLiqSyAshhBBCCLdbuvkTsvLSXdrXZodj+RbOFFnpTjjrGOPYFqpRMntQECNa+bh87evb+vBZVBHr04yOtv/bnsuVMRr81UrXn4SHvbunAEu53vh2gSrGtHX9dRBCNB+SyAshhBBCCLfLykvn2NmDLu+vBGIUOM1/T4zS8GFiMFG+qjpdW6FQ8EY/HQOWZWD+p3P/TJGNN/7K56XeTWOI/ZlCK1+mFjq1PdEtAJVSeuOFuBhJIi+EEEIIIRqcSunFNf1uJyo0Bm+1FpPFxJHT+/ht5wqsNovzvgp4vlcgj3T1P+/EtX2Qmge7+PPOngJH2+x9Bdwe70uHIPUFPZeG8O6efEzlZhi09ldxSztfzwUkhPCopjOWSAghhBBCNBs6/xD6JwwnIjgGX40/kSExjLz8TiaOfMZpP61Kwc/XhvN4PfQ+P9U9gOhyvfkWOzy9VY/dXkPZ+0Ygw2Dl80OVe+PV0hsvxEVLeuSFEEIIIUSDyyvM5sNl0zlxNhWb3YZGreWhG6fTKiKOQL9g8gpLitP1CPXmsvDqq9LXhb9ayat9dYxfl+1oW59mZOkxA2Muaby92+/vLaDYWvY42lfFbXGNN14hhPu5nMgvWrSoxu0KhQKtVkvLli3p3r07Go3mgoMTQgghhBDNk8Vq4Vh62Zx5o7kYo6kIBQpUyrKfqF71PH50dBstQ1tqWHemfOE7PVfGaAlohIXvsoqtfJzi3Bv/SII/GpX0xgtxMXM5kZ88eTKKf5a2qDj8qHy7QqEgICCAJ554gkcffbQeQxVCCCGEEM3NyMvvICq0DX4+AUSFtiblxF/k5Ge67XoKhYL/9NPRf2lZ4bu0fwrfvdwIC9/N2VdIYblS9S18lIxr7+fBiIQQjYHLtx03bNhA586dGTRoEAsWLGDTpk1s2rSJzz//nIEDB5KQkMBPP/3EggUL6N69Oy+99BIff/yxO2MXQgghhBBNXKuIOCJCYwjTRWKxmtEXZNd+0AWK16l5qIu/U9sH+wpIyTW7/dp1kWu08dGBAqe2h7v64+MlvfFCXOxcTuTnzJlDZGQky5YtY9SoUXTp0oUuXbowevRoli1bRlhYGF9++SUjR45k6dKl9O7dWxJ5IYQQQghRozlLX2L655N5c/FT5ORn0qfzMC6J6uD26z7VPYAYP+fCd1O25DaqwncfHSggz1wWT4hGyYQO0hsvhKjD0PoffviBF154ocptCoWCq6++munTpzNr1iyUSiWjRo1i+vTp9RaoEEIIIYQ7Ld38CVl56XU+LjQwkusHTHBDRBeX3IIsUk7sIikinviYbvyd5vqa8+fDT61kRh/nwncb001897eBG2M9X0gu32xjzn7n3vgHu/jj1wjn8QshGp7LibzdbufQoUPVbj948CA2W9nilhqNRgreCSGEEKLJyMpL59hZ9yaPokzrFnF4qbw4mpYCgK/Gn/iYrhSbDE5F8NxpdBstw1pqWFuu8N1z2/UktfJ84buPDxSSYyzrjdd5K7i3k/TGCyFKuJzIjxgxgo8//pg2bdrwr3/9C1/fkjuVRUVFfPrpp3z66afccMMNjv2Tk5OJjY2t/4iFEEIIIRqASunFNf1uJyo0Bm+1FpPFxJHT+/ht5wqsNounw2tyiq3OQ9YTYvswpOcocgqysFjN+Gr8CfAL4sjpfRw6ubtBYiotfHd5ucJ36QYbr+/MZ3ofzxW+KzTbeH+fc2/8pM7+BHpLb7wQooTLifzrr7/OsWPHeO6553jxxRdp0aIFABkZGVgsFi699FJef/11AIqLi9FqtTz44IPuiVoIIYQQws10/iH0TxhOkSEfo7mYkEBfOrXuSVx0Fz5cLtMH68JotXMw10L51HjT7p/w0foRpotCpfIiO+8s+5N3smXfmgaNLU6n5pGu/ry1uyxxnrO/gNvjfekcrG7QWEp9fqiIc8VlI10D1Aomdfav4QghxMXG5UQ+ODiYn3/+mRUrVrB27VpOnjwJwPDhwxk2bBgjR45EqSy5S6jVannvvffcE7EQQgghRAPIK8zmw2XTOXE2FZvdhkat5aEbp9MqIo5Av2DyCnM8HWKT8X/b9eSbbejKFVvXF2Wz5Ld5nguqnCe6BfC/IwZOFVoBsNphytZcVo4Icyyz3FCKLXbe25Pv1Daxox/BGumNF0KUcTmRh5LhR6NHj2b06NHuikcIIYQQolGwWC1Oc7WN5mKMpiIUKFAp6/QT6qL29ZEiPk4pZCjh8M/o+lCNko7BalxJkUMDI90aH5QUvpvZV8dda8sK321ON7HkqIGb2zVs4bsvUwtJN5T1xvt6KXiwq/TGCyGcyb9CQgghhBA1GHn5HUSFtsHPJ4Co0NaknPiLnPxMT4fVJKTkmnns91wA1jEGgLYBKn4b1YKgRtbDPLK1liujNfxyuqzw3fPJeq5qpW2wuekmq5139jjPjb+7gx9hWlU1RwghLlZ1qlr/2Wef8cUXX3Ds2DFyc3Mr7aNQKMjKyqrP+IQQQgghPKpVRByhugi0ah8sVjP6guzaDxIUmG2MW5tNkaWsyJ1GBZ8PDWl0STyU/I59vW8Qly89i+mfDvGzBhuv/ZXHq32C6u06xgPvYCs6XeW2swYrb/tb4J8OeKUCLlN4Y9ihQOkbjabTY/UWhxCiaXM5kX/hhReYPXs2CQkJ3HLLLQQFBbkxLCGEEEKIxmHO0pcACPIPZeLIZ+jTeRg7Uze5fZ3zpsxut/Po5lwO6Z2r+7/RL4juod4eiqp27XRePJIQwJu7yuaof7i/kDvi/OgSUj+F72xFp7Hp91S5LRwI11ZozAdbVTsLIS5qLifyixYtYvTo0Xz22WduDEcIIYQQonHKLcgi5cQukiLiiY/p5kjkLZJlVfJxSiHf/m1wars9zpe74ht2vvn5eKKbP/87UsTJgrLCd09tzWXV1W4qfKdQoY0Zjk9UIkp1AHZrMcbMPyg88g2SwgshquPyuKbi4mKGDBnixlCEEEIIIRqP1i3iiI3q6Hjsq/EnPqYrxSaDUxG8nedMbD1rrOoUF6UdmSae3a53ausc7MWbl+savAL8+fD1UvJahTXkt5w18fVRQzVHXBhtyyEE93oe79AElJpgvHRxBHZ5kJB+/3HL9YQQzYPLPfKJiYn8+eef/Otf/3JjOEIIIYQQnmG02p0eJ8T2YUjPUeQUZGGxmvHV+BPgF8SR0/s4dHJ32XE2O9f8eI6nuwfwVPcAvJSNP1l1l+xiK+PXZWMu15EcoFawYGgIvl6Nb158da5prWXFqU/wzSyby67epUAdrsarlpsRtsgYjBOmuHwtqyGTouMryD8wH5sxC6W3jtAB7+EdmoBXQCyW/KPn/TyEEM2Xy4n8W2+9xY033sibb77JuHHjaNGihTvjEkIIIYRoMLlGG/tzzASXa9u0+yd8tH6E6aJQqbzIzjvL/uSdbNm3ptLxNju89lc+69OMfJQYTCv/i29hIJvdzv0bchxrsZd6f2Awcbr6mV/eUBQKBYPIxF+f4rwhp/6vZc7ejT677MaQzaTHUngSdVB7VH7RksgLIark8r8yPXv2xG638+qrr/Lqq6+iVqtRKp3vrCoUCs6cOVPvQQohhBBCuEuxxc7tv2YRYbETXK6zVV+UzZLf5tXpXFvOmhi4LIP3BgRzXVufeo60cfvv7gLWnHaeYvBAZ78m+zr4qKroeR+YhKLXABQhLcDHF9uc6XAstcbzFFvs7M0xs/OciZ3nzNxpMNG9hl/gCpUPXv5tsRSlY87ee4HPQgjRXLmcyI8ZM6ZJzGsSQgghhHCV1Wbn/o3Z/H7WxFDC4Z/R9WEaJR2C1NT20yfHaONIXhCU64TWm+yMX5fN3R18mdFH16SGlJ+v9WeKeXVnnlNbn3BvXrpMV80RTZNywpPgr4PiIhSBwRAcXimRLzDb+PJgIX/+k7jvzzFTbgU+xkTYq/8FrlAR3HcmXv6tKPz7O2wmNwwBEEI0Cy4n8nPmzHFnHEIIIYQQDcput/Psdj3LjhUDsI4xAFwe4c0HSWH4eLnWgZFhsGLcmMOvFXqjPz1YxJazJuYPDqFrPS1d1hidKbQycX0OtnLJaqhGySdDgvGuqle7CbMv+xL7oT0orhuHot/QKvf5K8vMo7/nnsfZlQT3mYEmrBfF6RvJ2/PeBcUqhGjeLr4JXEIIIYQQwLt7CvjoQKFTWwedF19dEepyEg/QwkfFN8NDmb2vgJd35DkVekvJtfDe979ymX8xUb6qSscaDAZSUlIqtQPodDoSExNdjsMTzDY796zPJrO47EkrgHmDg4lphnUC7Mu+KPmfa8fW85mVBPeZjjaiP8UZW8nZ/m8cw0OEEKIK1f6F3bx5MwADBgxwelyb0v2FEEIIIRqrxYeLmLbDeSh4S18lS5JCCdbUfSi8UqHg4a4BDIrUcM/6bI7klY21D7EVoMjLIT2v6mP1en3VG5qAl3fkseWsyaltao8AhkVrPRRR49TaX0WvMG96hqlJKFCD00p2CoJ7v4I2ciDGzGRytj2LrB8vhKhNtYn8yJEjUSgUpKen4+3t7XhcHbvdjkKhIDs72y2BCiGEEELUh7Wni3lok/Pc40BvBd8MD7vgavM9wrxZP7oFT2/V89Xholr312g0jB49GrVazbp160hLS7ug6zekFccNzNpb4NR2RbSGp3sEeCiixsFbqeCa1lpH4t4jVE2otmw0hmGHElu5RN63zSi0UYOwWYpQ+YQTPuSTkg1KFfkHPqH4zNoGfgZCiKag2n+tVqxYAYC3t7fTYyGEEEKIpuqvcybGrc12Kj7mrYSFw0LpUk/z2P3VSj4YFMzQlhqe2JILlur3TUpKIiYmBpVKRUBAQKNI5I0H3sFWdLrGfYqtdvyzTHwTUdZ21h7F1YlPo7zIiyP3aeHNV1eEury/1XgOU85+sDsv24dChd1S+80gIcTFqdpEfuDAgTU+FkIIIYRoSo7lW7h5TRYF5bJ4BfBhYjCDojT1fr2b2/nSu4U3C79Vgrny9ri4ONq0aYPJZMLHp/Es0WYrOo1Nv6fGfbyBPhVeskJf555n4Rpj+u8Y03/3dBhCiCam+VUhEUIIIYSo4FyxlRtXn3Mqygbwah8dYy7xddt12wZ4kRCq5my6c7tarWbgwIHo9XpycnLo2LGj22K4YAoV2pjh+EQlolQHYLcWY8z8g8Ij31B+LneAuvkvs1cflL7RDXqcEKJ5qjaRf/311+t8MoVCwdNPP31BAQkhhBBC1KdCs41b12Q5FaADeKSrPw908Xf79asaaD58+HD8/PxYunQpPXr0cHsMF0LbcgjBvZ7HZsrBZtSjUPuhadEXTXhvsrc+5enwGpTyuXchPBJ8Sj43yrufgPGPYt+8Bvs38106h6bTY26MUAhxsag2kX/ttdfqfDJJ5IUQQgjRmFhsdib8ls2Oc85j22+J9WHaZYEeialt27bExsZy+PBhTp8+3egTeashk6LjK8g/MB+bMQult47QAe/hHZqAV0Aslvyjng6xwdjzclD4+EJBHvbMM+Xacz0XlBDiolRtIp+Tk1PdJiGEEEKIRs9ut/PY77n8fMro1D6kpYb3BwZ7pCibQqEgMTHRsX58dHS0Y358SEgIQUFB5ObmNnhcNTFn70afvdvx2GbSYyk8iTqoPSq/6IsrkZ81TVZ3F0I0CjJHXgghhBBs2LDhvNYz1+l0JCYmuiGi6rlSVR3gRIGF6wqtXPdPZfWj5ki+ZCILhobgrfJMZXW1Wo2vry9+fn7ccMMNAI7lffv370+7du1YuHChR2JzlULlg5d/WyxF6Ziz93o6HLexRcY06HFCCFEXdU7kc3Nz+e233zhx4gQArVu3ZsiQIQQFBdV3bEIIIYRoIHq9nvT09Np3bARcqaoOEAPEaMsea1UKlgwKJdDbc0XZzGYzycnJeHmV/QSLj48nMjKSgwcPkpKS4rHYXKJQEdx3Jl7+rSj8+ztspuY7gtM4YYqnQxBCiGrVKZF/9913ee211zAajdjtZQOLtFotzz77LI888kidLr5582ZmzZrFrl27SEtLY/bs2dxxxx1AyT9006dPZ82aNRw7doyAgAAGDRrEiy++SKtWrWo87zfffMO7777LkSNHCAgIYMiQIbzyyitERETUeJwQQgghKtNoNIwePRq1Ws26desaxVrnTlysqt4lWE2Ir2eXR7Pb7ezYscOpLSwsjMjISFJTUzly5IiHInOFkuA+M9CE9aI4fSN5e97zdEBCCHHRcvmW9IIFC5g2bRp9+/Zl0aJF7Ny5k507d7J48WL69evHtGnT+OKLL+p08cLCQjp37sxrr71Waf3UoqIidu3axVNPPcX69ev56quvOH36NDfddBMWi6Xac27dupX777+f2267jS1btrBw4UJSUlK499576xSbEEIIIUokJSURExNDy5YtCQgI8HQ4lZRWVfcOTUCpCcZLF0dglwcJ6fcfp/18PDScvjYZGRmcOXOG/Px8p/bGNRdbSXCf6Wgj+lOcsZWc7f+msUUohBAXE5d75OfOncvgwYP5/vvvHXO5oKTyalJSEtdffz1z5szhrrvucvniSUlJJCUlATB58mSnbTqdjqVLlzq1vf322/Tr14+DBw/SpUuXKs+ZnJxMy5YtefDBBx3x3XfffUydOtXluIQQQghRIi4ujjZt2mAymSrddG8smnpV9eTkZJKTkyu1nyqwVrG3JygI7v0K2siBGDOTydn2LOVHOgghhGh4LvfIHz16lGuvvdYpiS+lUCgYOXIkR4+69x/K0jvVNc3H79u3L2fPnuXHH3/EbreTlZXFd999x/Dhw90amxBCCNHcqNVqBg4ciF6v5/jx454Op1rm7N3o/3odmzELKKuqrvQOROUX7eHoSjonIiMjq/yvdFtEZCSZ3qEcIdjx35+FWjakGWu/QD2z2Jx72n3bjEIbNQibpQiVTzjhQz4hfOjnhF/xJdqWwxo8PiGEEHXokdfpdBw7dqza7ceOHUOn09VHTFUymUw8//zzjBgxgujo6v9R7tOnDx9//DH33XcfBoMBi8XC0KFDmTNnTo3nT01Nrdd46/t8QjQU+eyKpko+uxfGYDBUahs+fDh+fn4sXbq02rXODQZDg7/2oQYDmhq2V1dV3WAwcMoDn5OoqCiioqJq3a9TVY0FJ2jokEONxU6vr9V4DlPOfrBXGCGgUGG3FDkeeur1FZ4jf3dFU9bYP7/x8fE1bnc5kR8xYgTz5s2jW7du3HLLLY6eebvdzjfffMP8+fO57bbbLizaalgsFu677z70ej2LFi2qcd+UlBSmTp3KlClTGDZsGGfPnuXf//43jz32GB9++GG1x9X2QtVFampqvZ5PiIYin13RVMln98KlpKQ4LT/Xtm1bYmNjOXz4MKdPn642kffx8Wnw196Q54PNVM3GGqqqeyLW2lT87K49XcyNq7OcZp8PjtLwXVIoKqV75/jb7XYe2pzL9XlK+per9m9M/x1j+u+1Ht8YX1/hPvJ3VzRlzeHz63Ii/+KLL5KcnMwDDzzAv//9b2JjY4GSIffnzp2jY8eOvPjii/UeoMVi4Z577mH//v2sXLmSkJCQGvf/73//S69evRwV9Lt27Yqvry9XX301L7zwQo29+UIIIYQomTKXmJiIwWAgJSWF6Ohox/z4kJAQgoKCyM3N9WyQVWr6VdWHRWt5snsAb+4qK3y3Ps3IG7vyeaZnoFuv/d7eAhamFtEtJNLRpvNW0iVY7dJcTKWv/MYSQoiG4nIiHxISwrp16/j0009Zs2YNJ0+eBCAhIYGrrrqK8ePHo9HUNNCt7sxmMxMmTODAgQOsXLnSpeXjDAYDKpXz0jKlj202KcwihBBC1EatVuPr64ufnx833HADgGMkXv/+/WnXrh0LFy70ZIhVaD5V1Z/pEcCWs0Y2p5cNO3j9r3wuj9AwuGX9/tYqteK4gWl/5AEwNXs8AJcEqPhlWDh+Ws8u2SeEEKKyOq0jr9FomDRpEpMmTaqXixcUFDgK5NlsNk6dOsXu3bsJDg4mKiqK8ePHs3PnThYtWoRCoeDs2bMABAYGOnoG7r//fgDHsPkRI0bw6KOP8vHHH3PFFVeQnp7Os88+S/fu3Wtdf14IIYQQJTfSk5OT8fIq+5kQHx9PZGQkBw8eJCUlxYPRVaV5VVX3Uir4eHAIg5ZlkFlc8jzswL0bstk4ugURvvWbWP91zsR963OcbnvovBV8PTyUUEnihRCiUapTIg9gtVrZtWsXJ06cAKBNmzZ0794dpdLlAvgOO3fuZNSoUY7HM2fOZObMmdx2220888wzrFq1CoAhQ4Y4HTd79mzuuOMOAE6dOuW07Y477qCgoIB58+bx/PPPExgYSGJiItOmTatzfEIIIcTFonyhcrvdzo4dO5y2h4WFERkZSWpqKkeOHGng6GpWVVV1AJQq8g98QvGZtZ4N8DxE+qqYNziYMT+XzZfPMNiYuD6bpVeF1dt8+TOFVm77NQuDtewD4KWABUNDiNep6+UaQggh6l+dEvnvvvuO5557jrNnz2K3l/zBVygURERE8OqrrzJmzJg6XXzQoEE1zrFzZf7dDz/8UKnt/vvvd/TUCyGEEKJ2JwosaGvYnpGRgU6ncywF25i4WlW9qRnSUsuUHgH856+y13xjuon/7Mrn2XqYL19gtjH2lyzSipxHL7x1eRCDW9b0aRBCCOFpLifyP/zwAxMnTqR9+/Y88cQTtG/fHoBDhw7xySefMHHiRDQaDddcc43bghVCCCFE/fvrnInThVba1bBPcnIyycnJDRZTXbhaVb0pmto9gN/TjWwqN1/+P3/lc3mEN0MuINm22e3ctyGH3dlmp/aHuvgzvoPfeZ9XCCFEw3A5kX/rrbfo0aMHq1atQqst+4dj8ODBjBs3jhEjRvDmm29KIi+EEEI0IWabnYc359Je4e+oDadRKugZ7o3qn9HbmQYbh/RlCZ+XUkHvcG+UCtDpdA0ec2l19AO5ZrKMZb3JEVoV8brqf9o0xarqKqWC+YNDSFyeQYah3Hz59TlsvK4Fkec5X37aH3msOlHs1HZ1Ky0vXebeyvhCCCHqh8uJ/IEDB3jxxRedkvhSGo2GW2+9lZdeeqlegxNCCCGEe32wr4A92Wb2qBIcbYuvDGFEKx/H42KLnY7/SyPXVDaP+tOEYK67xLdBYy2l6fQYZ4usJH2djqXc3P6frgnDJ8I9Vd09KdJXxbzEYK4vN18+s7hsvrxXHefLLzhUyHt7C5zaEkLUzBsc7Pa16oUQQtQPlxN5Hx8fsrKyqt1+7tw5RyV5IYQQF6+lmz8hKy+9zseFBkZy/YAJbohIVOdonoWZO/Oc2m68xMcpiQfQeim4tZ0vHx4odLQtOFTEGA8l8gBfHS5ySuI76Lzo28LbY/G42+CWWp7uEcDr5ebLb0o38fpf+TzXy/Ve9A1pRp74PdepLdJHyeIrQ/FX171wsRBCCM9wOZEfPHgwH374IUOHDqV///5O27Zu3cpHH33ElVdeWe8BCiGEaFqy8tI5dvagp8MQtbDb7Ty6OYficvXhgjUKXutb9VD5u9r7OSXy684YOZZvoW1AnRfAuWA2u50Fhwqd2sZ18HOsdd9cPd09gC1nTWxIMzra3tyVT/8Ib4ZG1z5f/rDezLi1WU43QHxUChZdGUq0nywzJ4QQTYnL//q+9NJLbNmyhZEjR9K9e3fi4+MBSE1NZdeuXURERMgSb0IIISpRKb24pt/tRIXG4K3WYrKYOHJ6H7/tXIHVZvF0eBetL1OL2FiugBrAjN46wn2qTui6hqi5NEzNjnNlc+W/TC3i+Tr0BteXjWkm/s4vuwPhrYSx7Zr/qECVUsG8xGAGVZwvv6FkvnxUDfPls4ut3LImy2l6BMDcxGB6hjXfkQxCCNFcuTyGqnXr1mzatIlJkyZRUFDA8uXLWb58OQUFBUyePJmNGzfSunVrd8YqhBCiCdL5h9A/YTgRwTH4avyJDIlh5OV3MnHkM54O7aJ1tsjK88l6p7YhLTXcFlfzUPmK1cy/Si3EYrNXs7f7VOyNH9XGh1DtxdGjHOGrYv7gEMpPZT/3z3z56t4Lk9XOXeuyOZrvvDzfC5cGcl3b5n8DRAghmqM6jYcLCwvj1Vdf5dVXX3VXPEIIIZqZvMJsPlw2nRNnU7HZbWjUWh66cTqtIuII9AsmrzDH0yFedKZu06Mv1zPro1LwTv+gWoemj7nEh2e36Sn8Z2z2mSIbv5wurjSn3p2yi62sOG5wahvX/uJaLi0xSsPUHgG0XvQ27Q1pjvbsjSra+Dv/tLMDJ/UWXjaUJfGHfKLYMPIRHk/wb6iQhRBC1LOGn9gmhBDiomKxWjiWXjZn3mguxmgqQoEClVL+GWpoPxw3sPSYcyL8f70CXJrrHqBWcsMlPnyRWuRoW3CoqEET+cVHDJjKVpzjkgAVg6IuvqHhT3UL4NiXZ+muTylr1Fe9b6d//isV6K3kRhdu3AghhGi86vQL6uDBgyxcuJBjx46Rm5uL3e48hEuhULB8+fJ6DVAIIUTzMPLyO4gKbYOfTwBRoa1JOfEXOfmZng7roqI32Xhqa65TW49QNQ90dr1ndlx7P6dE/ueTxaQXWc97PfO6sFdV5K69H8qLMCFVKRW0D/KCil+hgUkoeg1AEdICfHyxzZkOx1KddukU5IVFdfG9ZkII0Zy4nMgvXryYBx98ELVaTVxcHEFBQZX2qZjYCyGEEKVaRcQRqotAq/bBYjWjL8j2dEgXnZd35JFWVNadrVLAewOC6rQO+WXhajoHebE/t6RQodUOiw4X8Xi3gHqPt6LtGSZScssKJHop4PZa5vU3Z95VvG/KCU+Cvw6Ki1AEBkNweKVEXq1UIGUmhRCiaXM5kX/ttdfo1q0bS5YsITQ01J0xCSGEaIbmLH0JgCD/UCaOfIY+nYexM3UTf6fJUnUNYctZIx+nOPdmP9LVn26hdRuWrlAouKu9H89uLxvHveBQIY8m+Lu9Z/zzQ0VOj0e00hLRACMBmhL7si+xH9qD4rpxKPoN9XQ4Qggh3MTlqvXp6enceeedksQLIYS4ILkFWaSc2IWvxo/4mG6eDueiUGyx8+jmXKe2doEqnu5xfkvH3drOB+9yvyD+zreyqcJSdvVNb7Lx/d/Oc/srVtEXYF/2BRz4CyzufT+EEEJ4lss98l26dCEtLa32HYUQ4iK1YcMG9Ppqqk3VQKfTkZiY6IaIGofWLeLwUnlxNK2kKJevxp/4mK4UmwxORfCaG+OBd7AVna7zcUrfaDSdHqvXWN7anc8hvfNg6ncHBOPjdX496CFaFaPb+rDkaFli/cWhQhKjNBcUZ02WHC3CYC2bwhfjp2JYS/ddTwghhGjMXE7kZ8yYwb/+9S+uvPJK+vXr586YhBCiSdLr9aSnp3s6jEYnIbYPQ3qOIqcgC4vVjK/GnwC/II6c3sehk7sd+1lsNZykCbIVncam3+PpMNiXbebt3flObePb+zIw8sKS4Lvi/ZwS+eXHDfzHaCNY4/Jgvzr5/KDzsPo74n1R1WFuvxBCCNGcVJvI33zzzZXaAgICuOaaa4iLiyMmJgaVynlemkKh4Ouvv67/KIUQoonTaDSMHj0atVrNunXrLqoRTpt2/4SP1o8wXRQqlRfZeWfZn7yTLfvWOO23P8dModmGn9o9iaDHKVRoY4bjE5WIUh2A3VqMMfMPCo98A7jnLobVZufR33OwlKtFG+Gj5KXLdBd87kFR3rQNUHEsv2R9cqMV/nekiEl1qIDvqr/OmdidbXY8VgB3xl+8Re6EEEKIahP5lJSUKtcXjYmJobi4mMOHD1faJuuRCiFE1ZKSkhw3QAMCAi6qRF5flM2S3+bVul+e2cada7NZfGUomma4NJa25RCCez2PzZSDzahHofZD06IvmvDeZG99yi3X/OhAIX9kmp3a3ugXRFA99JorFQruivfjlT/zHG0LDhZyfye/ev898HmFJeeujNbQyr9OK+gKIYQQzUq1/wru2eP54YBCCNEcxMXF0aZNG0wmEz4+Pp4Ox+1CAyM5mmfhTJHV0aZVKbg0zJvy+Z3VDvuzzejNJb3RuYSz7oyRe9dn88mQkDotidYUWA2ZFB1fQf6B+diMWSi9dYQOeA/v0AS8AmKx5B+t1+sdz7cwvVySDTCytZbRbevvM3h7vC+v7syjdOr6/lwLf54zc2l43Srh16TAbHMawg8wTorcCSGEuMjJ7WwhhHAjtVrNwIED0ev15OTk0LFjR0+H5Hb9e41n0pF0isu1vdcviHHtKydfepON0T+dY1dWWa/x8uPFPPZ7LrMGBDWrkV7m7N3os8tqAthMeiyFJ1EHtUflF12vibzdbueJLbkUlhtTH6hW8MblQfV2DYAoXxVJMVp+PFn2bn9+qLBeE/nv/zaQby57Hi18lIxopa238zc3yufehfBI8CmZ4qC8+wkY/yj2zWuwfzPfw9EJIYSoLy6PrVu1ahVTpkypdvuUKVP46aef6iUoIYRoLoYPH46fnx9r167FbrfXfkAzMHtvAcVlnfFE+6oY267q+cw6byXfJoUSr3O+r/xlahHPJ+c169dMofLBy78tlqJ0zNl76/Xc3xw18Otpo1Pby711RLlhzfVx7Z3f22+PGsg319+c/wUVhtXfEeeLupmN1qhP9rwcKMiDzDPY9/4B/zy25+V6OjQhhBD1yOUe+VmzZhEbG1vt9uLiYt59911GjBhRL4EJIURT17ZtW2JjYzl8+DCnT5+mR48eng7J7XKMNj5OcU68Hknwx7uGOe9hWhXfJ4UyYtU5ThWW3QGYva+AIG8FU85zrfNGTaEiuO9MvPxbUfj3d9hMOY5NGQYrIWYbAedZ9O9csZVntjkvg9g/wrtSwl1fhsdoifJVklZUkrwXWux8/7ehyhEYdbU/x0xyhTn+9XHe5sw+axrN9/aXEEKIUi4n8vv37+eGG26odnv37t1ZuXJlvQQlhBBNnUKhIDExEYPBQEpKCtHR0Y758SEhIQQFBZGbm+vZIN1g7v4CCsoN5w7XKl1KvGL8vVh6VShXrzpHZnFZb+6MnfnovJXc54ZK6J6jJLjPDDRhvShO30jenvecth7Ks3DXojSSYrTcGOtLUozWab33pZs/ISuv+mUOD+VaGGwsuyGiVEAPqzfLf4/i+gET6v3ZeCkV3BHnx5vllrhbcKiwXhLuzw863xRKjNJwSaDMCixli4xp0OOEEEI0Hi7/a2ixWCguLq52u8FgwGg0VrtdCCEuJmq1Gl9fX/z8/Bw3QUvne/fv35927dqxcOFCT4ZY7/JMNubuL3Bqe6irv1MSWpM4nZpvk0IZ+dM58kxlNwOe3qZHp1FyazXD85sWJcF9pqON6E9xxlZytv8bqug/LbaW1ApYfryYALWCa1pruSnWlyEtNWTlpXPs7MFqr+ANxFR4yTOywNfF9+F83Nne1ymR/yPTzL5sM11C1Od9zmKLnf8dcV47frybRhU0VcYJ1U95FEII0by5nMh37tyZlStX8tBDD1UqPmSz2VixYsVFUcRJCCFcYTabSU5Oxsur7M9sfHw8kZGRHDx4kJSUFEd7cxkG+0lKIfpyCXiQt4IJHevWK9st1JuvrwxlzM9ZGKxl55q8MeefhLYpV/1XENz7FbSRAzFmJpOz7VlcWT8+32znf0cM/O+IgRCNkrFKC+VnuquUXlzT73aiQmPwVmsxWUwcOb2P33auwGqzuO3ZlNc2wIvBURrWp5Xd0P8itZDX+gad9zlXHDeQW+7zFKJRMrJNU37/hRBCiPrj8gS8SZMmsX37du666y527dqF0WjEaDTy119/ceedd/LHH39w//33uzNWIYRo1Mon5Ha7nR07drBt2zbHfzk5JfOgU1NTOXLkiGPflBwzxZamnc4XWWy8v8+5N35SZ//zmufdL0LDF8NCKH+o1Q53/5bNhrSmM/Kr4jvq22YU2qhB2CxFqHzCCR/yCeFDPyf8ii/Rthzm2E9bQz2BbKONNIPVqU3nH0L/hOFEBMfgq/EnMiSGkZffycSRz9Tn06lVxd7y/x0puqDPdcW148fG+aCp4bURQgghLiYu98jfeOONHD16lNdee41Vq1Y5bVMoFEydOpVbb7213gMUQoim4li+hZr6CzMyMtDpdOTn5zu1Zxtt3PJLFguvCDnvAmee9vnBIs6Vm9seoFZw/wXMa78yRstHicFM+C3HkRAbrXD7L1msuDqMnmH1t7yZu6QVWYks99hqPIcpZz/YnRNxFCrslrIh5JeGebOmZzhLjhax9JiBs4aae+3zCrP5cNl0TpxNxWa3oVFreejG6bSKiCPQL5i8wpwaj68v17bxIViTS46x5B3LMdpZecLATbF1Hw5/RG9hU7rJqU2K3AkhhBBl6lQxZsqUKdx8882sWLGCY8eOASVVmUeNGkXbtm3dEJ4QQjQN8w4UcKbQSrsa9klOTiY5ObnKbRvSjIz5+RzfDA8jWNO0knmj1c6svc43J+7p6HfBz2PMJb7kmew8+nuuo63AYufG1VmsuiaMjkHnP//a3fZlm0kvsBCpKWszpv+OMf33Wo9VAL1beNO7hTev9tGxKd3Et38XsfyY81DzUharhWPpZXPmjeZijKYiFChQKRuuMJxGpWBsO1/m7C/rSV9wqOi8EvmKS871beHdqN9vIYQQoqHV+V/4tm3b8vDDD7sjFiGEaJJ+Omlg6jY9YxT+jvHU3koF3ULV1Q4FNlnt7MsxU2Sxk6ko6bn+I9PMtasy+e6qMCLdsN63uyw6XMSZorJeYx+Vgge71E+V+fEd/Mg12XjxjzxutO4h3F4AFvjqWwUJoWrHMPTS1QGqotPpSExMrJd4XGGw2Ll3fTbjlZHY/vk8eCmgZ6i3S0PDlb7Rjv9XKRUMbqlhcEsNb/YLYu2ZYtZtUkEVMwxGXn4HUaFt8PMJICq0NSkn/iInP7O+npZLxrX3c0rkN6QZ+TvPUqdK8yarna8OOxe5c9fSeUIIIURTdd636g8fPsz3339Peno67du35/bbbycgIKA+YxNCiEbvr3Mm7vktB5sdvlUlAODnpWDVNWF0D615+PeQYis3rcli57mydbL351q4elUmS68Ko01A419my2Kz8/Zu59748R18CfepvxsRjyYEkGu0YdhZQDv+GSZug9wKOaper698sAe8+Iee/bkWpjLe0fbx4GCCzqNnujxvlYIRrXw4HeTFsbOVt7eKiCNUF4FW7YPFakZfkH1B1zsfnYLV9An3Zntm2bD4L1ILeeFSncvn+PFksdMShIFqBde3lSJ3QgghRHk1/kqcN28ec+bMYfXq1YSFhTnaV69ezbhx45yWm/voo49Ys2YNISEh7otWiItIbWtFVyc0MNIta0WLyk4VWBj7SxaF5Qp6KRXw6ZCQWpN4gFCtimVXhXHbr1lsLjcf+O98KyNWZfL9VY17+DjAkqMGjheUzflWK+HhrvV/U/eFSwN596AKiqrertFoGD16NGq1mnXr1pGWllbvMbhi9cliPjrgPCz81nY+3HiBSbwr5ix9CYAg/1AmjnyGPp2HsTN1E3+nVb9UnTvc1d7XKZFfmFrE//UMxEvpWqG6isPqb27ni18TrR0hhBBCuEuN/zL++OOPtG3b1imJt1qtPPLIIygUCmbNmsXvv//OtGnTOH78OP/973/dHrAQF4vStaLr+t/5JP+i7vJMJQXq0isUIvtPXx1JrbQunyfQW8mS4WFcVeGYtCIb16w6x85zpmqO9Dyb3c5/K/TG3xHnS7Rf/U8LUCgUxNYwPDspKYmYmBhatmzpsdFhGQYrD25yLizXxl/FG/2CGjSO3IIsUk7swlfjR3xMtwa9NsCYS3zwL7dm/VmDjdWnil069ni+hbWnnecNyLB6IYQQorIaE/mDBw9y2WWXObX9/vvvnD17lkmTJnHnnXfSqVMnHn30Ua6//npWr17t1mCFuJiplF6M6j+O+0b9Hw/d8DL3jX6eKy4d06DFrEQJs83Ov9Zlsz/HeY3uB7v4M7FT3eeG+3gp+HJYCDfFOg8fzjbaGP3TOTalN84l11YcL+aQvuw1UCngsW7uS6Kr68+Ni4ujTZs2mEyeu+lht9t5aFOO05BwlQLmDQ4m0Nu9vcmtW8QRG9XR8dhX4098TFeKTQanIngNxV+trPRZ/vxQNUMpKvgytchp2b4eoWqXRrcIIYQQF5saM4CsrCxatWrl1LZ+/XoUCgWjRo1yau/bty8rV66s/wiFEEDZWtFFhnyM5mJCAn3p1LoncdFd+HD5dE+Hd9Gw2+08tSWXtWeck+uRrbW80jvwvM+rVir4cFAwgWolnxwsG1qcb7Zz0+pzfD40tFKvvSfZ7Xbe2OXcG39TrA9tG3hev1qtZuDAgej1enJycujYsWPtB7nBvAOFrD7l/Jl4ukcAfVpoqjmi/iTE9mFIz1HkFGRhsZrx1fgT4BfEkdP7OHRyt9uvX5Vx7f34rFzyvuZUMWcKrbSsYbSGxWZnYarzsPrxsuScEEIIUaUaf3GFhoaSlZXl1LZlyxa8vb3p2rWrU7tWq0WtbtxzOYVoyhrLWtEXu3f3FFTqXbw0TM1Hg4NRKlybA1wdlVLBW5fr0HkreHtPgaO92Ap3/JrFh4nBDTLX2hWrTxnZm11WpE8BPOHG3vjqDB8+HD8/P5YuXUqPHj0a/PoA+3PM/PsP50J7/Vp482QDvR6bdv+Ej9aPMF0UKpUX2Xln2Z+8ky371jTI9avSM0xNl2Av9v0zasVmh68OF/FU9+pfk19OFzutfuDrpeDGWClyJ4QQQlSlxkS+a9euLFmyhAcffBC1Ws2pU6dITk5mwIABeHs7D3U7evQokZGRbg1WiItZY1kr+mL2/d9FTNuR59TW2l/FoitD8fWqn+HTCoWCFy/TEeit5KV/rjUnZT7tDWnwJ+QGehHl4tJ0tsgYjBOm1Etc5dntdt7c5fw6jG6rpUMDF+Zr27YtsbGxHD58mNOnT3skkS+22Jn4WzbGsnp/BKoVfJgY7HJxtwulL8pmyW/zGuRarlIoFIxv78fT28pucHxxqJAnuvlXe8Pr84PON8huuMTH7dMShBBCiKaqxl//Tz31FFdddRUDBw6kZ8+ebNq0CYvFwuTJkyvt+9NPP9GzZ0+3BSqEKNEY1oq+GG07a2TSRudRDzpvBd8MD6VFPS61VurxbgHovJU8uSWX9oY0Buv/WSO9EaywtiHNRHKm2amtoXqfSykUChITEx3rx0dHR+PjU9J7GxISQlBQELm5uW6PY9qOkqXmynvr8iC3Lh0YGnh+N83P97jzdUs7X/79h95xk+N4gZUNaUaGtKw8RSStyFqpIJ4MqxdCCCGqV+Mvjd69e/Ppp58yc+ZMli5dSuvWrZk9ezbDhw932u+3337j5MmTTJ061a3BCiEax1rRF5u/8yzc/qtzr6taCV8MC3VrL/SEjn4EeitQ7Kxi48AkFL0GoAhpAT6+2OZMh2OpboulvIq98VfFaOjWwAXJ1Go1vr6++Pn5ccMNNwAlyT1A//79adeuHQsXLgTAaLVXe54L8cupYubud57TfUusDze3c+/0h6ayvGSQRsl1bXz4+qjB0bbgUFGVifzC1CLKv02dg7y4LFym6wkhhBDVqbXL4LrrruO6666rcZ8hQ4Zw6tSpegtKCFG9xrJW9MUiu9jKzWuyyDI6LzP3bv8gEqPcX8jsplhfDMHqSj3xyglPgr8OiotQBAZDcHiDJPLbzhrZmO5cHf7JGuY9u4vZbCY5ORkvr7J/xuLj44mMjOTgwYOkpKQ42ndlmQk/U8zgKhLI85VpsDK5wlJzrf1VvHF5UL1dozm4q72fUyK/8riBrGIrodqyUSw2u50vKqwdP66Dn+PGjBBCCCEqk8lnQjRRnl4r+mJgtNq5Y202h/Och04/3SOA2+MbbthviKbyn2r7si+xvTgJ+/6/GiwOgLcqrBs/OErTIJXZK7Lb7ezYsYNt27Y5/svJKUmsU1NTOXLkiGNfs83OmNVZvL07H7v9wnvn7XY7D23OJcNQdnNHqYB5icHoZE63k4GR3sQGlCXtJhssPmJw2mdDmpHjBWXDXTQquNXNoxqEEEKIpk4qZAnRRLRuEYeXyoujaSU9jZ5eK7qpW7r5E7Ly0qvdbgdScy1EFlsZU649JDCSZ3tMcnt8tbEv+6Lkf64d22DX/OucqdISa57oja9ORkYGOp2O/Pz8SttsdnhpRx47Mk3MHnRhCff8lEJ+Puk8n3tK9wD6RjT8DY3GTqFQMK69n1ORyC8OFTK5c1mPe8Uid6Pb+BBcxc0rIYQQQpSRRF6IJqIxrhXdlGXlpXPsbM03QLyBmAqje1v7aC7aIb//rdAb37eFN4MiG3ZufE2Sk5NJTk6ucZ+VJ4pJWZHJF8NC6BRc9znYB3LM/DvZeZ5Dn3BvpjSiGxqNzW1xvrzyZ55jDnxKroXkTBN9Wmg4V2xl5QnnHvpxUuROCCGEqJUk8kI0Ea6uFe2mul7NnkrpxTX9bicqNAZvtRaTxcSR0/v4becKrLayofUNtKJYo3Mgx8zy48690E92C2jQmxo6na7abQaDwVG1vrwcow19nnNP+eE8C1eszGTWgCBujHV9CHexxc7E9dkUlyt6GKBW8NHghltqrimK8FUxopWWH06UfX4WHCqiTwsNiw4XYS5XfqJdoIqBjejmkBBCCNFYSSIvRBPh6lrRR/QW7Hb7RdtrfL50/iH0TxhOkSEfo7mYkEBfOrXuSVx0Fz5cPt3T4Z2X+ryn83aF3vhuIWqGxzTsUPLExMRqt6WmphIfH1/1cfkW9q3NZnd22ZJ5RRY796zP4Y9MEy/31qF2IRF/+U89+3Kc6yW8eXkQbd241FxzoPnkDeYfP8H+nLLXX/kXqNd7c0WWmf6Wsk9q2wAvfA+WzKm3RcZgnDClocMVQgghmoRqf30kJibywgsvcOWVVwKwaNEi+vfvT5s2bRosOCEuZqGBkVhssD3TiK1cRpYQonbM77UDh3ItZJbrIswtDuHTg0VM6CjDU+sirzCbD5dN58TZVGx2Gxq1lodunE6riDgC/YLJK8yp/SSNTEquGV+D9YLXuf87z8KSv52HPz/ZvWF74y9E2wAvfr42nKe25rIw1Xk+9pz9hfyVZebTISFE+lb/Oq09XcwH+5wrq98c6yNF2VygTD9F+LE9DK64IRf6VGzTV2wQQgghRFWqTeT37dvHuXPnHI8ffPBBPvzwQ0nkhWgg1w+YwKcphXybketoaxug4pPREU4JVIHZxpUrM0nJLesp3Lwtlx6hanqFyxBVV1msFqeigUZzMUZTEQoUqJRNs8c1q9jGsO8zeLOfjjGX+Jx34v32nnynm0kddF6MalN/S7k1BB8vBe8PCCqZz741F1O54dzj1n9Axup0QoK8qiyCZ7bZCTtn5tdyL4JGpaCrNRYGS4/xeRmYhKLXABQhLcDHF9uc6Q2yfKIQQgjRXFT767R169asXbuWkSNH4u/vL0N1hfCARYedew/HtvOt9D30VytZMDSEYSsyKfhniKrJBuPWZbNhdDgh2gvrjb3YjLz8DqJC2+DnE0BUaGtSTvxFTn6mp8OqRPncuxAeCT7+JY/vfgLGP4p98xrs38x37JdttDFhfQ5Ljxl46/IgwuvYO3+qwFLpc/hk9wCUTfDfA4VCwfgOfiSEqBm3LptThSUjWdob0uivT4FqBl2ogP5VtFszvDFU0S5qp5zwJPjroLgIRWAwBIdLIi+EEELUQbXru9x333188803tG7dmpCQEBQKBffddx8hISHV/hcaGtqQsQvRrB3RW9ieaXJqGxtX9TDe9kFqZg0Mcmo7VWjlvg052Oph3eyLSauIOCJCYwjTRWKxmtEXZHs6pCrZ83KgIA8yz2Df+wf889iel1vl/suPF9Pv+wy+/7uoyu3VeW9vgVMxsrYBKm64pHJRuaakV7g3v40OZ3BUDXP8ByaheOQllNPmoHz9c2hb9fx7cX7sy77E9uIk7Pv/8nQoQgghRJNUbY/8Aw88QM+ePdm0aRMZGRnMnz+fIUOG0K5du4aMT4iL1qIjzgnX5RHeNRbVGnOJL9syTMzdXzaP95fTRt7Ylc/UHoFui7O5mbP0JQCC/EOZOPIZ+nQexs7UTfydVvNSdQ3NPmtarcXsKvaZZxlt3P1bWe98WC2jNTIMVhYccp4X/kS3gGZRoT1Mq+K7pFBm7MyDnZW3S4+xe9mXfVHyP9eO9WwgQgghRBNV48TPfv360a9fPwDmzZvHbbfdxs0339wggQlxMbPZ7SyuMJz5tmp648t7+TIdO8+Z2ZZR1pP/2s58Lgv35oropjWn2Z3sdjvH8i017pNbkEXKiV0kRcQTH9PNo4m8LTLmvI7rGBxNj1A1f2WZndqXHStmU1oGb10exPU19K7P3lvgtNRatK+Ksc2ouJtKqeCFS3UULVNXKrJmX/Yl9kN7UFw3DkW/oZ4JUAghhBCiGi5XcMrJaXoVm4VoqjanmxzzdwG0Kri+be3Dmb1VCj4dEkLi8gzOFZeMh7YD967PYf3ocFr5N82ibfXJZLXz8OYcTIVWYsp1LLduEYeXyoujaSkA+Gr8iY/pSrHJ4FQEzxPOdwkuX+AXm5139xTw2l95TkPks4w2zu5+m7/+ziA2wKvS8msWu53B50wMjChraxfghfUvFUbfaDSdHjuvmBqjUG3lWWbSYyyEEEKIxqzOv+pXr17N6tWrOXHiBFBSFG/EiBGOZeqEEBeuYnGxkW18CKyimnZVWvqp+HhwMGNWZzkqjWcbbfxrXTarrglHo2r6w6LPl95kY9zabNanGRlTYVtCbB+G9BxFTkEWFqsZX40/AX5BHDm9j0Mnd3sk3vrgpVTwZPcArm6tZfLGHKfe+Vh1OvEcgnywVThOCfStOIXcDDZZHkwIIYQQwuNcTuSLi4sZP348a9asQalUEhkZCcDatWv55JNPGD58OAsWLECjqaF4kBCiVoVmG8uPOdfCdmVYfXmDW2p5vlcgL+/Ic7TtOGfm+e163rg8qD7CbHLOFFq5ec059uVUPaR+0+6f8NH6EaaLQqXyIjvvLPuTd7Jl35oGjtQ9OgerWTMynHd25/OfXflOvfMOChXamOH4RCWiVAdgtxZjzPyDwiPfUDnVF0IIIYQQnuJyIj9z5kxWr17N1KlTmTx5MoGBJcWz8vPzmTNnDq+99hqvvfYaL774otuCFReHDRs2oNfXvdtPp9ORmJjohoga1soTxY5l5AAifZQMqam6djUeS/BnW4aJn08WO9rmpRTSp4U3Nzejec6uOJBj5qbVWZwusla7j74omyW/zWvAqBqeWqlgSo9Arm7tw+SNladLaVsOIbjX89hMOdiMehRqPzQt+qIJ70321qc8ELEQQgghhKiKy4n8t99+y5133skzzzzj1B4QEMDTTz/NyZMn+eabbySRFxdMr9eTnp7u6TA8puKw+lva+aI6jyrhSoWCDwcFM3h5BscLyhLYR3/PpWuImk7B6guOtSnYmGbkjrVZ5Jmca7x7aSOIDvSuNDe8NqGBkfUZnkd0DVHz66hw/t6ognL3NqyGTIqOryD/wHxsxiyU3jpCB7yHd2gCXgGxWPKPei5o0awon3sXwiPBx7/k8d1PwPhHsW9eg/2b+R6OTgghhGj8XE7kMzMz6dmzZ7Xbe/Towddff10vQQlRHY1Gw+jRo1Gr1axbt460tDRPh1SvThVYWH/G6NRW12H15QVplCwYFkLSD5kY/0nYiix2xq3LZu2ocALUrs27b6q+PVrEAxtzMFUYFT6ilZZ3h0zC16t5P/+aqJUKWvl7Oc15N2fvRp9dVg/AZtJjKTyJOqg9Kr9oSeRFvbHn5aDw8YWCPOyZZ8q153ouKCGEEKIJcTmRj46OZsOGDUyYMKHK7Rs2bCA6OrreAhOiKklJScTExKBSqQgICGh2ifw3Rw1Oa4P3CL3wnvPuod680S+IRzbnOtpS9RYe3pTLp0OCUSiaX/E7u93O+3sL+PcfeZW23dPRj9f76prFWujuplD54OXfFktROubsvZ4Op0FJj7F72WdNw177bkIIIYSohsuJ/O23386MGTN4+OGHmTx5MnFxcQAcPnyYOXPmsGLFCp5//nm3BSpEXFwcbdq0wWQy4eNT+1JsTY3dbq80rH7sBfTGlzeuvR/bMkwsTC07/9JjBvrs92ZyF/96uUZjYbXZeXa7no8OFFba9uKlgTyW4N8sb17UO4WK4L4z8fJvReHf32EzXVxLkEqPcf2xRcY06HFCCCHExcDlRP6JJ57g+PHjfPnllyxcuNDxQ9hut2O327nrrrt4/PHH3RaouLip1WoGDhyIXq8nJyeHjh07ejqkevfnOTOH9GUV1b0UcFNs/d2weLNfELuyzHTI/JNwewEAJ3+HhSlqx9J2BoOBlJSUKo9vCsUEDRY7967PZuWJYqd2tRLeHxjMrRdZkb/zpyS4zww0Yb0oTt9I3p73PB1Qg5Me4/pjnDDF0yEIIYQQzY7LibxSqWTWrFlMmjSJ1atXc/LkSQBatWpFUlISXbp0cVuQQgwfPhw/Pz+WLl1Kjx49PB2OWyyu0Buf1EpLmFZVb+f38VLwxdAQ5n9dSFvKeleLsqH8lc9nxQB3Mh54B1vR6Vr3s9js7M+1MN5sY3wEHDVHMjV7PIFqBV8MC2FwS20DRNscKAnuMx1tRH+KM7aSs/3f0MxTWukxFkIIIURT43IiX6pLly6StIsG1bZtW2JjYzl8+DCnT59ulom80Wpnyd8VhtW7off4kkAv4nVemHOr3t4Yiwnaik5j0++pdT8l0FUFlLv30dJXydfDw+gacnFU6L9wCoJ7v4I2ciDGzGRytj3LxbB+vPQYCyGEEKKpqXMiL0RDUigUJCYmOoZ8R0dHO+bHh4SEEBQURG5urmeDrAc/nywmx1jW6xmsUXBVK/f0IIdqlVS3uF+TKCaoUKGNGY5PVCJKdQB2azHGzD8oPPIN5ZNOPy8Fq68NJ8Zf/sy5yrfNKLRRg7BZilD5hBM+5JOSDUoV+Qc+ofjMWs8GKIQQQgghAEnkRSOnVqvx9fXFz8+PG264AcBRn6F///60a9eOhQsXejLEerH4iHNv/E2X+KJRNWxBtqZSTFDbcgjBvZ7HZsrBZtSjUPuhadEXTXhvsrc+5dgvIURNgCTxdWI1nsOUsx/sVucNChV2S1HVBwkhhBBCiAYnv3JFo2Y2m0lOTsbLq+yjGh8fT2RkJAcPHqy2MFtTcq7YyuqTzsXZ6qtavauaUjFBqyGTouMryD8wH5sxC6W3jtAB7+EdmoBXQKxjrXMvqUxfZ8b03zGm/+7pMIQQQgghRC0kkReNmt1uZ8eOHU5tYWFhREZGkpqaypEjRzwUWf1ZctSApVwtsfY6L3qFNeyc7qZUTNCcvRt99m7HY5tJj6XwJOqg9qj8oh2JvKid0je6QY8TQgghhBD1QxJ50eRkZGSg0+nIz8/3dCj1omK1+tvifBt0nfOmXkxQofLBy78tlqJ0zNl7PR1Ok6Lp9JinQxBCCCGEEOdBeaEn2L59O2vWrKGwsLDOx27evJmxY8fSqVMngoKCnOY6m81mXnzxRfr370/Lli3p0KEDEydOdCx7VxOTycSMGTPo1q0bLVq0oGvXrsydO7fO8YnGKTk5ma+++qpSIbamuEDWgRwzf2WZHY8VwC0NuNa5K8UEGzWFiuC+M/Hyb0Xxmd+wmXJqP0YIIYQQQogmzuUe+TfeeINt27axZMkSR9ttt93Gzz//DEBUVBQ//vgjrVu3dvnihYWFdO7cmdtuu41JkyY5bSsqKmLXrl089dRTJCQkkJeXx/PPP89NN93E5s2bneZMVzRhwgTOnDnDu+++S2xsLJmZmRgMBpfjEp6l0+mw2OCPTBNWe1l63j5ITbi25N5TZrGNQ7lmp+MMloadV14fFlXojR/cUkO0X/2tHV+bpl1MUElwnxlownpRnL6RvD3veTogIYQQQgghGoTLifySJUu48sorHY9//PFHfvrpJx577DESEhKYOnUq//nPf3j//fddvnhSUhJJSUkATJ482WmbTqdj6dKlTm1vv/02/fr14+DBg9WuZb927Vo2bNjAzp07CQ0NBaBNmzYuxyQ8LzExkVl785mdnedoi/JVsvvGSNTKsiHnd6/L5vtjZTdoVHoYmGmiV7h3g8Z7vqw2O18fqTysviE13WKCSoL7TEcb0Z/ijK3kbP83TXNMhhBCCCGEEHXnciJ/5swZ4uPjHY+XL19Ou3btePHFFwFITU3lyy+/rP8IyymdE13TcN8ffviBnj17Mnv2bBYvXoxWq+XKK6/khRdewN/f363xifphtdmZd8B5qsY9Hf2dkniAty7X8ftZI2cNJWuHW+0waWMO60e3wMer8Vcs/y3NSLqhbN1zfy8FI1u7Z+346jTNYoIKgnu/gjZyIMbMZHK2PUv59eOFEEIIIYRo7lxO5BUKBVZr2drC69evZ9SoUY7HLVu2JDMzs36jK8dkMvH8888zYsQIoqOrr5h87Ngxtm7dikajYcGCBej1ep5++mnS09NZsGBBtcelpqbWa7z1fb6Lzbc9KrYUkZqaXmm/lZdWPvbU33mVGxuh1kDyQOe2M8fcnzjXNs2kumKCBoPBI5/rUIMBTbnHvm1GoY0ahM1ShMonnPAhn5RsUKrIP/AJxWfWOuI9Jd/Di4r83RVNlXx2RVMln13RlDX2z2/5TvSquJzIx8XF8cMPP3DPPffwyy+/kJ6ezvDhwx3bT58+7bbCWBaLhfvuuw+9Xs+iRYtq3Ndms6FQKJg3bx46nQ4omd9/ww03kJGRQYsWLao8rrYXqi5SU1Pr9XwXm5E/ZrIp3eR4fGe8L+8PDK52/4c35fBFatkQdQWw4uowBkZqqj3G0/JMNtovTqO47N4YK0aEMSjK/TGnpKSg1+ur3Z6cnExycnKldi+NtsE/17lGG3uOquhVbjU+q/Ecppz9YLc676xQYbeUfQ58fHzke3gRkb+7oqmSz65oquSzK5qy5vD5dTmRf/jhh7nnnnto06YNRUVFdOzYkSFDhji2r1+/nm7dutV7gBaLhXvuuYf9+/ezcuVKQkJCatw/IiKCqKgoRxIP0L59ewBOnTpVbSIvGoe92WanJB5gUueap0TM6KPjtzQjJwtKEjs7MHljDpuvb0GA+oIXZnCLpccMTkl8K38VAyIbZm5/+e9GRQaDAR8fH3JNNvZlOxcTPFmk5Xq7HWUDLY1nt9uZvCmHu612KJfIG9N/x5j+e4PEIIQQQgghRGPkciI/ZswYQkJC+PnnnwkMDGTixImOAlk5OTmEhoZy66231mtwZrOZCRMmcODAAVauXElEREStx/Tr149ly5ZRUFDgmBNfOs+3VatW9RqfqH9z9xc4PR4Y6U3XEHU1e5cI9FYye2Awo38652g7UWDlue163htQfU++J1WsVn9rO98GS5ATExOr3Vb+7uQrO/S8tbvc+1EM4fsKeLhrgLtDBOD9vQWsOlHM4JBIR1tLHxWxga792VL6Vj8FRwghhBBCiKbMpV/EJpOJ5ORkYmJiePXVVyttDw4OPq9CdwUFBRw9ehQoGRJ/6tQpdu/eTXBwMFFRUYwfP56dO3eyaNEiFAoFZ8+eBSAwMNCx1vX9998PwIcffgjATTfdxBtvvMGDDz7IM888g16v55lnnuG6664jPDy8zjGKhnOu2Mo3R50T3Np640slRmmY1NmPufvLiuQtOFTEta19uKpVwxaQq82xfAtbzjqPOritAdeOd9WzPQPZlG5iW0ZZrC/9kceACI3bVwbYctbItB0ltQ6mZo8HoFeYmh8Tw9GoGn8hQyGEEEIIIdzJpXHHXl5eXH/99axdu7ZeL75z504SExNJTEzEYDAwc+ZMEhMTefXVVzl9+jSrVq0iLS2NIUOG0KFDB8d/3333neMcp06d4tSpU47H/v7+LF26lLy8PIYNG8bdd9/NgAED6rQsnvCMzw4WYSw33LyNv4qr65CEv3ipjnid872pRzbnkF1sreYIz1hcoTe+T7g37XQuD45pMF5KBfMHB6PzLkucLXa4+7ds9Cb3VYnPNFiZ8Fs21nKryQV5K/h0SIgk8UIIIYQQQuBij7xSqaR169YUFBTUvnMdDBo0iNzc3Gq317St1A8//FCpLT4+nu+///4CIhMNzWyz83GK8+fr3k5+qJSuJ24+XgrmDgom6YdMRxJ41mBjylY9Hw+pubZCQ7Hb7Sz28NrxddHK34vZA4O5c222o+14gZXHNufyyZBgFPU8HcBqs3PvhhzSipxvFMxNDKZNQOO72SGEEEIIIYQnuFwJbNKkSXz22WduXWJOXLyWHTM4JW9+XgrujP//9u48PMrqDvv4PTPZE0IWYhJC2BN2RRArIGFRAaVWeaEoag0iIIgKxVAKoiyiCFrUKm+NKAUXQFEkSJWqZRHZVMpSBSGI7FsIWcieycz7R14GJoEkhCRPZvL9XFeuMudZ5jdwmvae85xz/K/6Pp3DvPTn653ncH/6W64++y3nClfUrK1nCnTo/MUnBLwt0sBmvgZWVL7fN/HVyDbO/xafHcrVe/ur/u/05V3ntf5EvlPb+A4B6h9du/+OAAAAgJpU4SGunJwc+fn5qVOnThowYICaNm3qmKd+gclk0lNPPVXlRcL9lVzk7oGWfgryrtyK83+5oZ6+Opqn3Zesuj5hS7q6hnsrws9yTXVeq5KL3N0Z7Vvpz1mTnr+pvraeLtD/Lvk7nbQtXTdf56U2wWUvRlhR647nac5O573ru4V7aWqnwCq5PwAAAOAuKhzkp0+f7vjzRx99dNlzCPKojB9TCvRjivNWZ6PaXv1o/AVeFpPeigtWr1VndGEqd1q+XeM2pWnZ7aFV/jh4ReVa7Vr5W65TW21+rP5SPh4mLewVrF6rUpRtLZ63kFdUPF9+7d1h8vO4ti8jTmQXaeS3abpkWrzCfMx6t1eIPK5iegUAAABQF1Q4yO/atas660AdVnI0/vYob8XUv7ZR3rbBnnqmU6Cm/ZjpaPv3sXy9n5yjh2Mr/yXBtfjiSK4yCy9G1TAfs26L8jaklsqIqe+pV7oGaczGNEfbL+lWTd6WodevYZu/Qptdj244p7N5F6dWmCS90zNYkQY/QQEAAADURhUO8o0bN67OOlBHncguKjVKXdEt58rzRLsAfXkkT1sv2T5tyrYM9Yz0NmThtJKP1f+xha/LjTYPbemnDSfytOzXi/9mi/fnqGekt/5P88o9XfD89sxS2/FNvrGeejasXdsGAgAAALVF7Z+cC7e28JdsWS95njqmvof6VNEotcVs0v/tESw/j4thOctq1+Pfpclmt5dxZdU7lVOktSUWcRva0pgnA67VK12D1DLQ+YuQcZvTdei89arv9cWRXP39J+cnMm6L8lbCDfWucAUAAACAqxqW3LNnjxITE7Vz505lZmbKZnPeIspkMmnnzp1VWR/cWJ7Vrn/uy3Zqe6yNv8xVOIe9eaCHnu8SqKe3ZDjaNp0q0Ft7svV4u6oZ+a+I5b/myHbJdwftQzzVIaRqFomraQGeZi3sFazbV6c41iA4X2jXI+vP6d93hcmrgnu9HzpvdXpMX5Ia+pn1dlxwlfYBAAAAwN1UeER+y5Yt6tOnj7788ktFRETo0KFDatq0qSIjI3X06FH5+/urW7du1Vkr3MzygzlKzb/4ZVCgl0n3V8Pib8Nb+atPQ+dR/pnbM7Q/vfAKV1Qtu91e6rH6+1u49nZq14d6aVaX+k5tO84Waub2zCtc4SzPatewdeeUUXDx2w0Pk/TPXiEK9WFePAAAAFCWCo/Iv/DCC4qOjtY333wjq9Wqli1basKECerZs6e2bdumIUOGaNasWdVZK9yI3W4vtcjdwzH+CvCs+tkeJpNJb9warK0vzFLTrJMXa9hlkk+ol8ob+7VFNFL+8ImVfv/d5wq1J/3iY+cWkzSkhWusVl+WkW38teFkvv51JM/R9ubPWeoR6a1+0WXPb5/6Q4Z2pjp/kTL9pkD9Ltx1Fv8DAAAAjFLhIL9z50795S9/Uf369ZWWVvw47IVH63/3u98pPj5eL7zwgvr06VM9lcKtfHeqQD+nXQy3ZlNxMKwuUf4W9bWkKDLjF+cDZ6vtLR1KjsbfHuWt63xdf9TZZDLpzVuDtSvpjI5lFznaH9+Ypo33XKeG/pf/jJ8ezNE7vzhPqfh9Yx+NrcGpDgAAAIArq/Dwp8lkUv36xY/S+vkVjyaeO3fOcbxly5bau3dvFZcHd1VyNP6uaJ9qX0k+7HLh+da+Mj01Q+bp/5B5zmKpaUyVvmehza5PDjqvyl8d0weMEuxt1js9g3XptPjUfJtGfXtORbbSCwruTy/UU5vSndqa1rPozVuDZWJePAAAAFAhV7X93KFDhyRJ3t7eatKkidatW6dBgwZJkjZv3qyQkJBqKRLu5dB5q748mufUNroGRmMvFxPNw5+WAupLeTkyBQZLwWHSoeQqe89vjuU57Y9e38ukO6Nde358SbeEe2vKjYFquGSeYnMvTl04t9GixgEXf8UU2e0qSi3Uqku2KTCZpNhWzRTgPalGawYAAABcWYWDfJ8+ffTZZ59p2rRpkqT4+HjNnDlTR44ckd1u13fffafx48dXV51wI+/szS61gnv3cC9DarEnfSD7/v/JdM/DMt3Su1L3yN/7mmw5xy97LCKjUMvDLwb5SF+L7Ls8lCvJ7Bcl7zbjK/Wetc34DgH6rei0Ol46dSHD+RyLpC6XubYo3Vu5l2kHAAAAcHkVDvJPP/20Bg0apMLCQnl6emr8+PEqKipSUlKSLBaL/vrXv2rChAnVWSvcQFahTe8lO8+PHt3W37DHqu1J7xf/YcD9lb6HLee4bBn/u+yxWEmxl677ZpdsGZc91aVZzCa1CvKQUkocuLWvTJ26yxRyneTrJ9s/ZlXpEw8AAABAXVThIB8UFKSOHTs6XptMJiUkJCghIaE66oKbWnYgR5mXbDnWwMeswc1q95zxM7lF+vVsgWLqe8i/IqvqmyzyaXSHfCPjZPasJ3tRnvJTflT2r8sl2cq93FV5mUt/GVPdUxcAAACAuqhSq4v9+uuvSklJUZs2bRwL4AHlsdntStzrPBo/rJW/fDxq9yJn+zOsuu3z4qHm6ACLWtf3UGyQp1oFeah1kIfa2O1Oq0b6NOyl4E5TZStIky0/QyZPf3lf9zt5h3XRua1164uvqpi6AAAAAMDZVW3avXz5crVv315dunTRXXfdpZ07d0qSUlNT1blzZ3322WfVUSPcxNrj+UrOuLjlnIdJerR19W05Vx2OZhXp6+P5mv9zlp7alK6+/zqrrWcKnM4pyk1RzuHPlbJ2mFLWPqSz64bJev43eYV2kEe95gZVbgx70vvS3p2StaDccwEAAABUTIWDfFJSkkaNGqXY2FjNnDlTdvvFx6NDQ0MVGxurZcuWVUuRcA8lt5wb2MxXkX6uv596SYXnditj5xzZ8lMlSbaCDFmzj8rsFSiLf5TB1QEAAABwdRUO8n/729/Uq1cvrVixQg888ECp4zfddJN++umnKi0O7mN/eqG+OZ7v1Da6bfVvOVcVQrzNahFo0WWmgFeIyeIrj4CmsuacUuE5/jsCAAAA4NpUeI78/v379cILL1zxeFhYmM6ePVslRcH9vF1ibnyXME91DjNmy7lLmZ95XQqLkHyLv1QwPzJBih8n+6avZV/+jiSpbbCntg+KUJ7VrgOZVu1LL9S+jP//n+nWy+5P72CyKPh3s+UREK3s31bIVpBW/R8KAAAAgFurcJD38/NTdnb2FY//9ttvCg0NrZKi4F7S821aeiDHqa22jMbbM9Nk8vWTsjJlTzlxSXt6qXN9PExqH+Kp9iGeTu3Z271L7ZlezKzgm1+Qd4NOyju1UZn/+3vVFg8AAACgTiozyNtsNpnNxU/fx8XFacmSJRo9enSp806ePKnFixfrrrvuqp4q4dLeT85WtvXimgoN/cz6Q1NfAyu6yP7GdNnLP61MZl1uUzmzgm+eJZ/wbso7s1Vp3z8rXfM7AQAAAEA5Qb5nz55644031LFjR02dOlW33367evXqpXvvvVcmk0lff/211q1bp8WLF8tisWjSpEk1VTdcRJHNrgUlHqt/tHWAPCs74fwa2CIa1dB1JgV3eV4+EbcqP+UHpW2bLHfeP74sFZm6AAAAAODqlBnk09LSdPvtt2vkyJGaOnWqvvrqK02aNEkvvfSS7Ha75s+fL0nq0aOH5s2bp+jo6BopGq7ji6N5OpJV5HjtY5GGtfIzpJb84RNr5H38mtwtn8gesllzZPENU1ivhcUHzBad37tQeSfW1kgdtcHVTF0AAAAAUDFlBvlt27bphRde0Ntvv63Vq1frlVde0Weffab09HQdPHhQNptNTZs2VYMGDWqqXriYklvO/bG5n0J93G/LuUsV5Z9VQdoeyV7kfMBkkd2ac/mL3FRVTF0AAAAA4KzMIO/v768XX3xR9913nyZMmKChQ4fqnnvu0dy5c9WpU6eaqhEuandqgTadKnBqe6yWLHJXnfJPbVb+qc1Gl1Hjam7qAgAAAFC3VWjV+htuuEHffPON3n33Xc2cOVOdO3dWZGRkqfNMJpO2bt1a5UXCNSWWmBt/a4RXqRXf3YHZL6pGr6utamrqAgAAAFDXVXj7uYKCAp04cUK5ubkKDQ1VWFhYddYFF7By00KlZp667LFCm115KQUaeElbmzxPvfulWaGBEbq3+/CaKbIGeLcZb3QJAAAAAOqQCgX5DRs26M9//rMOHz6s4cOH67nnnlO9evWquzbUcqmZp3To9L4rHm8oSZcsTn8+o/gHAAAAAFB5ZQb5c+fOafLkyVq+fLlat26tNWvWqEuXLjVVG1yMxeyhu255QJGhjeTl6aMCa4F+Pf6z1u/4XEU2q9HlAQAAAIBbKDPI33TTTcrNzdUzzzyjcePGycOjwk/iow6qHxCibh3uUE7ueeUX5ikk0E9tGt+ollHtlLhqltHlAQAAAIBbKDOZt2/fXq+99pqaN29eU/XAhWVmn1Ni0iwdOZ0sm90mb08fPTFolqLDWyrQP1iZ2WlGlwgAAAAALq/MIL9q1aqaqgNuwFpk1aFTF+fM5xfmKb8gRyaZZDHzNAcAAAAAVAXSFarc77s+qMjQJvL3rafI0Mb65chOpZ1PMbosAAAAAHALBHlUuejwlgqtHy4fT19ZiwqVkXXO6JIAAAAAwG0Q5FHl/rFyhiQpKCBUI37/V93cto92JH+n305eeas6AAAAAEDFmI0uAO4rPStVvxzZJT9vf8U0ut7ocgAAAADALRDkUWn2Eq8bX9dSzSNbO177eQcoplF75RXkOi2CBwAAAACoPB6tR6UdzSpyet2h+c3qdePdSstKlbWoUH7eAarnH6Rfj/+s/Ud3G1QlAAAAALgXgjwqZeEv2TqSZVUj08W273avka+PvxrUj5TF4qFzmae154cd2vLz18YVCgAAAABuhiCPq5Z0KFdPb0nXvSXaM3LO6ZP1C4woCQAAAADqDII8rsrGk/kaueGc7JLSFSbZJYvJpHbBHgr0qtiSC6GBEdVbJAAAAAC4MYI8Kmx3aoEe/E+qCmzFr9dpoCwmacltoeoX7WNscQAAAABQR7BqPSrk0HmrBn+dqsxC57Xq3+geRIgHAAAAgBpEkEe5zuQWaeC/z+pMrs2pfcZNgXogxt+gqgAAAACgbiLIo0znC23649ep+u2881ZzY9sF6Kn2AQZVBQAAAAB1F0EeV5RfZNdD/zmnXamFTu1Dmvvq+S6BMplMV7gSAAAAAFBdCPK4LJvdrtHfpmnDyXyn9tuivPXmrcEyE+IBAAAAwBAEeZRit9s1aVuGPjuU69TeuYGnFvcOkZeFEA8AAAAARiHIo5S/7c7Sgr3ZTm0x9T308R2hCvCkywAAAACAkUhlcPLe/mzN+m+mU1ukn1mf9g1VqI/FoKoAAAAAABd4GF0Aql/+3tdkyzle7nmp+TY1TC/U8vDi1wcLI/Ri1jB92reBGgfQVQAAAACgNiCd1QG2nOOyZfyv3POCJXX1ufjabJKW3haqtsGe1VccAAAAAOCqEOTrIpNFPo3ukG9knMye9WQvylN+yo/K/nW5JJvjtNb1PRUV4W1cnQAAAACAUgjydZBPw14K7jRVtoI02fIzZPL0l/d1v5N3WBed25rgOC/EmyUUAAAAAKC2IcjXQUW5Kco5/LnO731HtvxUmb3qK7T73+UV2kEe9ZrLev6g0SUCAAAAAK6AIF8HFZ7brYxzux2vbQUZsmYflWdQrCz+UQR5AAAAAKjFeHYaMll85RHQVNacUyo895PR5QAAAAAAykCQr+tMFgX/brY8AqKVd2K9bAVpRlcEAAAAACgDQb5OMyv45hfk3aCT8k59p8z//d3oggAAAAAA5SDI11lmBd88Sz7h3ZR3ZqvSvn9Wkt3oogAAAAAA5SDI10kmBXd5Xj4Rtyo/5QelbZusS/ePBwAAAADUXqxaXwf5NblbPpE9ZLPmyOIbprBeC4sPmC06v3eh8k6sNbZAAAAAAMAVEeTroKL8sypI2yPZi5wPmCyyW3OMKQoAAAAAUCEE+Too/9Rm5Z/abHQZAAAAAIBKMHSO/KZNm3T//ferTZs2CgoK0ocffug4VlhYqGnTpqlbt25q2LChWrVqpREjRujo0aMVvv+WLVsUGhqqrl27Vkf5LsPsFyVz/Q46aGqjzXmxjp9f7K1lrt/hyj9+UUaXDgAAAAAowdAR+ezsbLVt21ZDhw7V6NGjnY7l5ORo165dSkhIUIcOHZSZmampU6dq8ODB2rRpkzw8yi49PT1do0ePVs+ePXXy5Mnq/Bi1nneb8coqtOnOZaeUZb24Mv2S20LUubGvgZUBAAAAAK6WoUG+b9++6tu3ryTp8ccfdzpWv359rVy50qnt1Vdf1S233KJ9+/apXbt2Zd77iSee0NChQ2W327Vq1aoqrdsVrTyU6xTiw33N6tvIx8CKAAAAAACV4VLbz50/f16SFBQUVOZ577zzjlJSUjRx4sQaqMo1fLDfeRG7B1r6ycNsMqgaAAAAAEBlucxidwUFBZo6dar69++vqKgrz93++eefNWfOHH399deyWCwVvn9ycnJVlFlt97tWb8RKir20JUfJyWcMqga1WW3ru0BF0Xfhqui7cFX0Xbiy2t5/Y2JiyjzuEkHearVq1KhRysjI0NKlS694Xn5+voYPH67nn39eTZs2var3KO8v6mokJydX6f2u1bM/ZOiNn7Icr7tHeOlfd4YZWBFqq9rWd4GKou/CVdF34arou3Bl7tB/a32Qt1qtevTRR7Vnzx6tXr1aISEhVzz31KlT2rdvn8aOHauxY8dKkmw2m+x2u0JDQ7V8+XL16dOnpkqvFQqK7Fp6wPmx+odj/Q2qBgAAAABwrWp1kC8sLNTw4cO1d+9erV69WuHh4WWe37BhQ23e7Lw/+rvvvqt169bpgw8+UOPGjauz3FppzdE8nc2zOV4Hepn0hyasVA8AAAAArsrQIJ+VlaWDBw9KKh45P3bsmHbv3q3g4GBFRkYqPj5eO3bs0NKlS2UymXT69GlJUmBgoHx9i8PoY489JklKTEyUp6en2rZt6/QeDRo0kLe3d6n2uuL9/dlOr4c095OvB4vcAQAAAICrMnTV+h07diguLk5xcXHKzc3V7NmzFRcXpxdffFHHjx/XF198oZMnT6pXr15q1aqV42fFihWOexw7dkzHjh0z8FPUXseyrPrPiXyntodi/AyqBgAAAABQFQwdke/Ro4fS09OveLysYxf861//KvP45MmTNXny5KuszD0sOZAj28Wt43V9iKc6NvAyriAAAAAAwDVzqX3kUXE2u10fJDsvcvenWEbjAQAAAMDVEeTd1Lcn83Ukq8jx2sci/bE5QR4AAAAAXB1B3k29t995NP4PTXwV5M0/NwAAAAC4OpKdGzqXV6TVh3Od2v7E3vEAAAAA4BYI8m7oo19zVXBx63g1r2fRrREscgcAAAAA7oAg72bsdnupveMfivWXycTe8QAAAADgDgjybua/Zwu1J93qeG0xSUNbssgdAAAAALgLgrybKTkaf0cjH0X6WQyqBgAAAABQ1QjybiSr0KZPDjovcvcwe8cDAAAAgFshyLuRlYdylWW1O16H+5rVt5GPgRUBAAAAAKoaQd6NfFBi7/gHWvrJw8widwAAAADgTgjybmJfeqG2nilwansohr3jAQAAAMDdEOTdxAfJzqPx3SO81KK+h0HVAAAAAACqC0HeDRQU2bX0gHOQfziW0XgAAAAAcEcEeTew5miezubZHK8DvUz6QxNfAysCAAAAAFQXgrwbKLl3/JDmfvL1YJE7AAAAAHBHBHkXdyzLqv+cyHdqeyiGveMBAAAAwF0R5F3ckgM5sl3cOl7Xh3iqYwMv4woCAAAAAFQrgrwLs9ntpVar/1Mso/EAAAAA4M4I8i7s25P5OpJV5HjtY5H+2JwgDwAAAADujCDvwt7b7zwa/4cmvgry5p8UAAAAANwZqc9Fncsr0urDuU5tf2LveAAAAABwewR5F/XRr7kquLh1vJrXs+jWCBa5AwAAAAB3R5B3QXa7vdTe8Q/F+stkYu94AAAAAHB3BHkX9N+zhdqTbnW8tpikoS1Z5A4AAAAA6gKCvAsqORp/RyMfRfpZDKoGAAAAAFCTCPIuJrvQpk9/c17k7mH2jgcAAACAOoMg72JWHsrV+UK743W4r1l9G/kYWBEAAAAAoCYR5F3M+yX2jn+gpZ88zCxyBwAAAAB1BUHehexLL9TWMwVObQ/FsHc8AAAAANQlBHkX8kGy82h89wgvtajvYVA1AAAAAAAjkAJrGe+FL8t86lipdptd+mNKge61XZwfH1vfQ747ilert0U0Uv7wiTVWJwAAAADAGAT5WsZ86pgs+3aVardI6layMaMmKgIAAAAA1CYEeVdwa1+ZOnWXKeQ6yddPtn/Mkg4lG10VAAAAAMAABHkXYB7+tBRQX8rLkSkwWAoOI8gDAAAAQB3FYncuwJ70gWzTRsu+Z6fRpQAAAAAADEaQdwH2pPelvTsla0G55wIAAAAA3BtBHgAAAAAAF0KQBwAAAADAhRDkAQAAAABwIQR5AAAAAABcCEEeAAAAAAAXwj7yLsD8zOtSWITkG1D8+pEJUvw42Td9LfvydwyuDgAAAABQkwjyLsCemSaTr5+UlSl7yolL2tONKwoAAAAAYAiCvAuwvzFddqOLAAAAAADUCgT5WsYW0ahGrwMAAAAAuBaCfC2TP3yi0SUAAAAAAGoxVq0HAAAAAMCFEOQBAAAAAHAhBHkAAAAAAFwIQR4AAAAAABdCkAcAAAAAwIUQ5AEAAAAAcCGm9PR0u9FFAAAAAACAimFEHgAAAAAAF0KQBwAAAADAhRDkAQAAAABwIQR5AAAAAABcCEEeAAAAAAAXQpAHAAAAAMCFEOQrYcGCBerWrZuio6MVHR2tO+64Q//+978dx+12u2bPnq3WrVsrIiJCAwYM0N69ew2sGChWVt8tLCzUtGnT1K1bNzVs2FCtWrXSiBEjdPToUYOrBsr/vXup8ePHKygoSG+88UYNVwmUVpG+e+DAAT300ENq3LixIiMjFRcXp3379hlUMXBRef03KytLEydOVNu2bRUREaGbbrpJ8+fPN7Bi4PLmzZunoKAgTZw40dHm6pmNIF8JDRs21IwZM7RhwwatW7dOcXFxevDBB/XTTz9Jkl5//XXNnz9fc+bM0dq1axUWFqaBAwfq/PnzBleOuq6svpuTk6Ndu3YpISFBGzZs0JIlS3T8+HENHjxYVqvV6NJRx5X3e/eCpKQkbd++XZGRkQZVCjgrr+8eOnRI/fr1U5MmTbRq1Spt2bJFU6dOlb+/v8GVA+X332eeeUZfffWV3nrrLW3btk1PP/20ZsyYoWXLlhlcOXDRDz/8oEWLFqldu3ZO7a6e2Uzp6el2o4twB02bNtW0adM0bNgwtW7dWiNHjlRCQoIkKTc3VzExMXr++ef1yCOPGFwp4OxC371c3/zll190yy23aNOmTaV++QFGK9l3jxw5on79+mnlypUaPHiwRo0apSeffNLgKoHSLu27I0aMkMlk0oIFC4wuC6iQS/tv165ddffdd2vKlCmO43fddZfatWunl19+2cAqgWIZGRnq2bOn/v73v2vOnDlq27atXn75ZdntdpfPbIzIX6OioiJ9+umnys7O1s0336zDhw/r9OnT6tOnj+McX19fdevWTdu2bTOwUsBZyb57ORe+kQwKCqrByoCyXa7vWq1WjRgxQgkJCWrVqpXBFQKXV7Lv2mw2rVmzRq1atdKgQYPUokUL9e7dWytWrDC6VKCUy/3uveWWW7RmzRodO3ZMkrRt2zb99NNPuu2224wsFXAYP3687rnnHsXFxTm1u0Nm8zC6AFf1888/q2/fvsrLy5O/v78++OADtWvXzvEPHxYW5nR+WFiYTp48aUSpgJMr9d2SCgoKNHXqVPXv319RUVEGVAo4K6vvzp49WyEhIXr00UcNrhIo7Up99/Tp08rKytK8efM0ZcoUTZs2Td9++61Gjhwpf39/9evXz+jSgTJ/986ZM0fjx49X+/bt5eFRHCvmzp2r/v37G1kyIElavHixDh48qLfffrvUsdOnT0ty7cxGkK+kmJgYbdy4UZmZmUpKStKYMWO0evVqo8sCynWlvtu2bVvHOVarVaNGjVJGRoaWLl1qYLXARVfqu6mpqVqyZIk2btxodInAZV2p7wYHB0sqfhT5iSeekCRdf/312rlzpxYsWECQR61Q1v9vSExM1Pfff6+lS5cqOjpamzdv1rPPPqvGjRvr9ttvN7p01GHJycmaOXOm1qxZI09PT6PLqRbMka8i99xzj6Kjo5WQkKCOHTtq7dq16tSpk+P4kCFDFBISorfeesvAKoHSLvTdN998U1JxiH/00Ue1Z88erV69WuHh4QZXCFzehb4bFRWluXPnymy+OFusqKhIZrNZERER2rNnj4FVAqVd6Lvz5s1Tw4YNNWnSJKeVlOfOnasVK1Zo69atBlYJXN6F/vvyyy+rcePGWrRokQYMGOA4/uSTT+rIkSNKSkoysErUdR9++KHGjh0ri8XiaCsqKpLJZJLZbNbWrVvVpUsXl85sjMhXEZvNpoKCAjVp0kTh4eFat26do1Pk5eVpy5YtmjlzpsFVAqVd6LtS8RZ0w4cP1969ewnxqPUu9N0RI0bonnvucTo2aNAgDRo0SPHx8QZVB1zZhb7r5eWlTp06KTk52en4gQMHFB0dbVB1QNku9N/CwkIVFhY6BSVJslgsstlsBlUHFBswYIBuvPFGp7axY8eqRYsWmjBhglq2bOnymY0gXwnTp09X3759FRUVpaysLH3yySf67rvv9PHHH8tkMmnMmDGaN2+eYmJi1LJlS73yyivy9/fX4MGDjS4ddVxZfddqtSo+Pl47duzQ0qVLZTKZHPOHAgMD5evra3D1qMvK6rthYWGl5rh5eHgoPDxcMTExBlUMFCur70rSU089pUceeUTdunVTXFycNm7cqBUrVujDDz80uHKg7P4bGBio7t27a8aMGfL391d0dLQ2bdqkZcuWacaMGUaXjjouKCio1GLNfn5+Cg4OdkwndfXMRpCvhNOnT2vUqFE6c+aMAgMD1a5dO33yySeOFTrHjRun3NxcTZw4Uenp6ercubNWrFihevXqGVw56rqy+u7hw4f1xRdfSJJ69erldN38+fP14IMPGlAxUKy837tAbVVe3/3973+v1157TfPmzdNf//pXNW/eXG+99Rbz41ErlNd/Fy5cqBkzZmjUqFFKS0tTdHS0nnnmGY0aNcrgyoHyuXpmY448AAAAAAAuhH3kAQAAAABwIQR5AAAAAABcCEEeAAAAAAAXQpAHAAAAAMCFEOQBAAAAAHAhBHkAAAAAAFwIQR4AAFSpDRs2KC4uThEREQoKClJ6enqV3LdDhw4aM2bMNd9nzJgxCg8Pr4KKAAAwBkEeAACD3X333WrWrJnOnj1b6lhWVpbat2+v7t27y2q1GlDd1Tl//rzi4+NlNps1d+5cJSYmyt/f/7Lnbty4UUFBQU4/TZo0Ue/evfX+++9fUx0nT57U7NmztXv37mu6DwAAtZGH0QUAAFDXvfbaa+revbumTJmit99+2+nYiy++qBMnTmjx4sXy8Kj9/7P9008/KT09XRMnTtSAAQMqdM3IkSN10003SZLS0tL0+eef68knn1RqaqrGjx/vOO/HH3+U2VyxMYhTp05pzpw5aty4sa6//vqr/hwAANRmjMgDAGCwFi1aKCEhQR9//LHWrVvnaN+1a5cSExM1YsQIde7cuVprKCoqUn5+/jXfJyUlRZIUGBhY4WtuueUW3Xfffbrvvvs0evRorVq1Ss2bN9fy5cudzvP29panp2eZ9yooKHCJJxcAALgWBHkAAGqBcePGqW3btvrzn/+s3Nxc2Ww2TZgwQREREXr22Wd14MABDRs2TM2aNVN4eLh69OihpKQkp3ukpaXp2WefVbdu3dSoUSNFRUVpwIAB2rx5s9N5hw8fVlBQkF599VW9/fbb6tSpk6677jp9//33ZdaYlJSkXr16KSIiQs2aNdOjjz6qo0ePOo4PGDBADz/8sKTi6QJBQUGVmtNusVgUGhpa6gmEknPkLzya//HHH2v27Nlq3769IiIi9NFHH6l3796SpLFjxzoe2589e7bT/U6cOKEHHnhAUVFRatGihaZOnaqioqKrrhcAgJpW+5/RAwCgDvD09NRrr72m/v37a+7cuYqKitL27du1ZMkSnThxQn379lV4eLjGjRsnf39/rV69WvHx8UpMTNR9990nSTp06JCSkpI0cOBANW3aVBkZGXr//fd17733au3atWrfvr3Te3700UfKzs7WsGHDFBAQoIiIiCvW99FHH+mxxx5Tx44d9dxzzyk1NVWJiYnaunWrvv32W4WGhiohIUHt27dXYmKinn76acXGxqpZs2blfvasrCylpqZKktLT05WUlKQff/yxVPC+knnz5slsNuuxxx6TJN1xxx2aMmWKXnzxRQ0bNkxdu3aVJLVr185xjc1m0+DBg9WpUyc9//zzWr9+vd58803HFxQAANRmpvT0dLvRRQAAgGIJCQlatGiRfH191bt3b7333nsaOHCgTp48qXXr1snX19dx7sCBA7Vv3z79/PPPMplMys/Pl6enp9M88vT0dHXp0kX9+/fXG2+8Ial4RP6GG26Qv7+/tm/fXmaAl6TCwkK1a9dOwcHBWr9+vaOGjRs36u6779YTTzyhWbNmSSoetY+Pj9fnn3+uHj16lHnfC9eXZDKZNHHiRE2ZMsWpvUOHDrr11lv1j3/8w+n6Ro0aadu2bU6L6u3YsUO9e/fW/Pnz9eCDDzrdZ8yYMVq6dKkmT56sSZMmOdrj4uJkNpu1fv36MusGAMBoPFoPAEAt8txzzyk0NFR2u11z585VWlqa1q9fr3vvvVc5OTlKTU11/Nx22206ceKEDhw4IKl4DvmFEJ+Xl6dz586pqKhInTp10s6dO0u914ABA8oN8VJxKD5z5oyGDx/u9EVCjx491LFjR3311VfX9JkTEhK0cuVKrVy5Uv/85z81ZMgQzZ071/HFQ3nuv//+K66MX5b4+Hin1127dtWhQ4eu+j4AANQ0Hq0HAKAWCQwMVMuWLXXmzBlFRERo+/btstvteumll/TSSy9d9pqUlBTFxMTIZrPp9ddf16JFi3T48GGnc5o0aVLquqZNm1aopgvz4GNiYkodi42N1apVqyp0nytp06aNevXq5Xg9cOBAZWZmatasWbr//vsVFhZW5vUV/RyX8vT0LPUlRlXueQ8AQHUiyAMAUIvZbDZJ0uOPP66+ffte9py2bdtKKp4rPmvWLA0dOlRTp05VSEiILBaL5s2bp99++63UdZeOrtc2cXFx+vLLL/Xf//5X/fr1K/PcynyOim5jBwBAbUSQBwCgFrsw2uzh4eE0an05K1eudJpDfkFFF427kujoaElScnKy+vTp43QsOTlZjRs3vqb7X86FLeSys7Mrdb3JZKrKcgAAqFX4OhoAgFosLCxMPXr00OLFi3XixIlSx8+ePev4s8Vikd3uvIbttm3byt1Wrjw33nijrrvuOi1atEh5eXmO9s2bN2vHjh3ljphXxoV59yVX2q8oPz8/SeJReQCAW2JEHgCAWm7evHnq16+funfvrvj4eDVr1kwpKSn68ccftW/fPu3YsUOSdOedd+qll17SY489pm7duunXX3/VokWL1Lp1a2VlZVX6/T09PTVz5kyNHj1ad955p4YMGeLYfq5hw4YaP378NX2+rVu3Okbg09PTtWbNGm3cuFGDBg1SbGxspe7ZrFkzBQUFaeHChQoICFBAQIDatGnjmIYAAIArI8gDAFDLxcTEaN26dZozZ46WLVum1NRUNWjQQO3bt9czzzzjOG/ChAnKzc3V8uXLlZSUpDZt2mjhwoX69NNP9d13311TDffff798fX316quvavr06fL19dUdd9yh6dOnKzQ09JruvWDBAi1YsECS5OXlpaZNm+rZZ5/VU089Vel7enp6KjExUTNmzFBCQoIKCws1adIkgjwAwC2wjzwAAAAAAC6EOfIAAAAAALgQgjwAAAAAAC6EIA8AAAAAgAshyAMAAAAA4EII8gAAAAAAuBCCPAAAAAAALoQgDwAAAACACyHIAwAAAADgQgjyAAAAAAC4kP8HDOujOGrHHR8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,6))\n",
    "plt.plot(group_data[\"time_of_birth\"], group_data[\"years_of_schooling\"], zorder=-1)\n",
    "for q in range(1, 5):\n",
    "    x = group_data.query(f\"quarter_of_birth=={q}\")[\"time_of_birth\"]\n",
    "    y = group_data.query(f\"quarter_of_birth=={q}\")[\"years_of_schooling\"]\n",
    "    plt.scatter(x, y, marker=\"s\", s=200, c=f\"C{q}\")\n",
    "    plt.scatter(x, y, marker=f\"${q}$\", s=100, c=f\"white\")\n",
    "\n",
    "plt.title(\"Years of Education by Quarter of Birth (first stage)\")\n",
    "plt.xlabel(\"Year of Birth\")\n",
    "plt.ylabel(\"Years of Schooling\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remarkably, there is a seasonal pattern on the years of schooling that follows the quarter of the year. Visually, we can see that those born in the first quarter of the year have almost always less education than those born in the last quarter (once we control for the year of birth, after all, those born in later years have more education, in general).\n",
    "\n",
    "To be a bit more rigorous, we can run the 1st stage as a linear regression. We will first convert the quarter of birth to dummy variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>log_wage</th>\n",
       "      <th>years_of_schooling</th>\n",
       "      <th>...</th>\n",
       "      <th>q3</th>\n",
       "      <th>q4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.790019</td>\n",
       "      <td>12.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.952494</td>\n",
       "      <td>11.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.315949</td>\n",
       "      <td>12.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.595926</td>\n",
       "      <td>12.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6.068915</td>\n",
       "      <td>12.0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 9 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   log_wage  years_of_schooling  ...  q3  q4\n",
       "0  5.790019                12.0  ...   0   0\n",
       "1  5.952494                11.0  ...   0   0\n",
       "2  5.315949                12.0  ...   0   0\n",
       "3  5.595926                12.0  ...   0   0\n",
       "4  6.068915                12.0  ...   0   0\n",
       "\n",
       "[5 rows x 9 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "factor_data = data.assign(**{f\"q{int(q)}\": (data[\"quarter_of_birth\"] == q).astype(int)\n",
    "                             for q in data[\"quarter_of_birth\"].unique()})\n",
    "\n",
    "factor_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For simplicity, let's only use the last quarter, q4, as the instrument for now. We will run a regression of years of schooling, the treatment, on quarter of birth, the instrument. This will show us if indeed quarter of birth positively affects time of education like we saw in the plot above. We also need to control for years of birth here and we will add state of birth as an additional control."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q4 parameter estimate:,  0.10085809272786578\n",
      "q4 p-value:,  5.4648294166163044e-15\n"
     ]
    }
   ],
   "source": [
    "first_stage = smf.ols(\"years_of_schooling ~ C(year_of_birth) + C(state_of_birth) + q4\", data=factor_data).fit()\n",
    "\n",
    "print(\"q4 parameter estimate:, \", first_stage.params[\"q4\"])\n",
    "print(\"q4 p-value:, \", first_stage.pvalues[\"q4\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It looks like those born in the last quarter of the year have, on average, 0.1 more years of education than those born in other quarters of the year. The p-value is close to zero. This closes the case on whether quarter of birth causes more or less years of schooling.\n",
    "\n",
    "![img](./data/img/iv/incomplete-files.png)\n",
    "\n",
    "## The Reduced Form\n",
    "\n",
    "Unfortunately, we can't verify the second IV condition. We can only argue in favor of it. We can express our belief that quarter of birth does not influence potential earnings. In other words, the time people are born is not an indication of their personal ability or any other factor that can cause a difference in earnings, other than the effect on education. A good way of doing that is to say that the quarter of birth is as good as randomly assigned when we are thinking about it's impact on earnings. (It isn't random. There is evidence that people tend to conceive around the end of the summer or around some sort of holiday. But I can't think of any good reason that this pattern also affects income in any way other than through education).\n",
    "\n",
    "Having argued in favor of the exclusion restriction, we can proceed to run the reduced form. The reduced form aims at figuring out how the instrument influences the outcome. Since, by assumption, all this influence is due to the effect on treatment, this will shed some light into how the treatment affects the outcome. Once again, let's evaluate this visually before getting serious with regression. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,6))\n",
    "plt.plot(group_data[\"time_of_birth\"], group_data[\"log_wage\"], zorder=-1)\n",
    "for q in range(1, 5):\n",
    "    x = group_data.query(f\"quarter_of_birth=={q}\")[\"time_of_birth\"]\n",
    "    y = group_data.query(f\"quarter_of_birth=={q}\")[\"log_wage\"]\n",
    "    plt.scatter(x, y, marker=\"s\", s=200, c=f\"C{q}\")\n",
    "    plt.scatter(x, y, marker=f\"${q}$\", s=100, c=f\"white\")\n",
    "\n",
    "plt.title(\"Average Weekly Wage by Quarter of Birth (reduced form)\")\n",
    "plt.xlabel(\"Year of Birth\")\n",
    "plt.ylabel(\"Log Weekly Earnings\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, we can see a seasonal pattern on earnings by the quarter of birth. Those born later on the year have slightly higher income than those born in the beginning of the year. To test this hypothesis, we will again regress the instrumental q4 on log wage. We will also add the same additional controls as in the 1st stage:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "q4 parameter estimate:,  0.008603484260140015\n",
      "q4 p-value:,  0.0014949127183659584\n"
     ]
    }
   ],
   "source": [
    "reduced_form = smf.ols(\"log_wage ~ C(year_of_birth) + C(state_of_birth) + q4\", data=factor_data).fit()\n",
    "\n",
    "print(\"q4 parameter estimate:, \", reduced_form.params[\"q4\"])\n",
    "print(\"q4 p-value:, \", reduced_form.pvalues[\"q4\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, we have a significant result. Those born in the last quarter of the year have, on average, 0.8% higher wages. This time, the p-value is not so close to zero as before, but it's still pretty significant, being just 0.0015. \n",
    "\n",
    "## Instrumental Variables by Hand\n",
    "\n",
    "Having both our reduced form and our 1st stage, we can now scale the effect of the first stage by the reduced form. Since the first stage coefficient was something like 0.1, this will multiply the effect of the reduced form coefficient by almost 10. This will give us our unbiased IV estimate of the average causal effect:\n",
    "\n",
    "$\n",
    "\\mathrm{ATE}_{IV} = \\dfrac{\\text{Reduced Form}}{\\text{1st Stage}} \n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08530286492085315"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reduced_form.params[\"q4\"] / first_stage.params[\"q4\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This means that we should expect each additional year of school to increase wages by 8%.\n",
    "\n",
    "Another way to get the IV estimates is by using 2 stages least squares, **2SLS**. With this procedure, we do the first stage like before and then run a second stage where we replace the treatment variable by the fitted values of the 1st stage\n",
    "\n",
    "$\n",
    "\\mathrm{educ}_i = \\gamma_0 + \\gamma_1 \\times \\mathrm{q4}_i + \\gamma_2\\times \\mathrm{yob}_i + \\gamma_3\\times \\mathrm{sob}_i + v_i\n",
    "$\n",
    "\n",
    "$\n",
    "\\log(\\mathrm{wage})_i = \\beta_0 + \\beta_1\\times \\mathrm{educ}_i + \\beta_2\\times \\mathrm{yob}_i + \\beta_3\\times \\mathrm{sob}_i + u_i\n",
    "$\n",
    "\n",
    "$\n",
    "\\log(\\mathrm{wage})_i = \\beta_0 + \\beta_1 [\\gamma_0 + \\gamma_1 \\times \\mathrm{q4}_i + \\gamma_2\\times \\mathrm{yob}_i + \\gamma_3\\times \\mathrm{sob}_i + v_i ]  + \\beta_2\\times \\mathrm{yob}_i + \\beta_3\\times \\mathrm{sob}_i + u_i\n",
    "$\n",
    "\n",
    "One thing to notice is that **any additional control we add to the second stage should also be added to the first stage when doing IV**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0853028649208674"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iv_by_hand = smf.ols(\"log_wage ~ C(year_of_birth) + C(state_of_birth) + years_of_schooling_fitted\",\n",
    "                     data=factor_data.assign(years_of_schooling_fitted=first_stage.fittedvalues)).fit()\n",
    "\n",
    "iv_by_hand.params[\"years_of_schooling_fitted\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the parameters are exactly the same. This second way of looking at IV can be useful for the intuition it gives. In 2SLS, the first stage creates a new version of the treatment that is purged from omitted variable bias. We then use this purged version of the treatment, the fitted values of the 1st stage, in a linear regression.  \n",
    "\n",
    "In practice, however, we don't do IV by hand. Not because it is troublesome, but because the standard errors we get from this second stage are a bit off. Instead, we should always let the machine do the job for us. In Python, we can use the library [linearmodels](https://bashtage.github.io/linearmodels/) to run 2SLS the right way.\n",
    "\n",
    "The formula for 2SLS is a bit different. We should add the first stage between \\[ \\] inside the formula. In our case, we add `years_of_schooling ~ q4`. Additional controls don't need to be added to the first stage because the computer will do this automatically if we include them in the second stage. For this reason, we add `year_of_birth` and `state_of_birth` outside the formula of the 1st stage. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: 0.0853028649580665\n",
      "SE: 0.02554081280759766\n",
      "95 CI: [0.03524287 0.13536286]\n",
      "P-value: 0.0008381914592261452\n"
     ]
    }
   ],
   "source": [
    "def parse(model, exog=\"years_of_schooling\"):\n",
    "    param = model.params[exog]\n",
    "    se = model.std_errors[exog]\n",
    "    p_val = model.pvalues[exog]\n",
    "    print(f\"Parameter: {param}\")\n",
    "    print(f\"SE: {se}\")\n",
    "    print(f\"95 CI: {(-1.96*se,1.96*se) + param}\")\n",
    "    print(f\"P-value: {p_val}\")\n",
    "    \n",
    "formula = 'log_wage ~ 1 + C(year_of_birth) + C(state_of_birth) + [years_of_schooling ~ q4]'\n",
    "iv2sls = IV2SLS.from_formula(formula, factor_data).fit()\n",
    "parse(iv2sls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, we can see that the parameter is exactly the same as the ones we've got before. The extra benefit is that we have valid standard errors now. With this at hand, we can say that we expect 1 extra year of education to increase wages by 8.5%, on average. \n",
    "\n",
    "## Multiple Instruments\n",
    "\n",
    "Another advantage of using the computers is to run 2SLS is that it is easy to add multiple instruments. In our example, we will use all quarter of birth dummies as instruments for years of schooling. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: 0.10769370488924324\n",
      "SE: 0.0195571490089523\n",
      "95 CI: [0.06936169 0.14602572]\n",
      "P-value: 3.657974678716869e-08\n"
     ]
    }
   ],
   "source": [
    "formula = 'log_wage ~ 1 + C(year_of_birth) + C(state_of_birth) + [years_of_schooling ~ q1+q2+q3]'\n",
    "iv_many_zs = IV2SLS.from_formula(formula, factor_data).fit()\n",
    "parse(iv_many_zs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With all 3 dummies, the estimated return on education is now 0.1, which means that we should expect a 10% average increase on earnings for every additional year of education. Let's compare this with the traditional OLS estimate. To do that, we can use 2SLS again, but without the 1st stage now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameter: 0.067325728176578\n",
      "SE: 0.00038839984390487046\n",
      "95 CI: [0.06656446 0.06808699]\n",
      "P-value: 0.0\n"
     ]
    }
   ],
   "source": [
    "formula = \"log_wage ~ years_of_schooling + C(state_of_birth) + C(year_of_birth) + C(quarter_of_birth)\"\n",
    "ols = IV2SLS.from_formula(formula, data=data).fit()\n",
    "parse(ols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The return on education is estimated to be lower with OLS than with 2SLS. This suggests that OVB might not be as strong as we first though. Also, notice the confidence intervals. 2SLS has a much wider CI than the OLS estimate. Let's explore this further\n",
    "\n",
    "## Weakness of Instruments\n",
    "\n",
    "![img](./data/img/iv/weak-iv.png)\n",
    "\n",
    "When dealing with IV, we need to remember we are estimating the ATE indirectly. Our estimates depend on both the first stage and the second stage. If the impact of the treatment on the outcome is indeed strong, the second stage will also be strong. However, it doesn't matter how strong the second stage is if we have a weak first stage. A weak first stage means that the instrument has only a very small correlation with the treatment. Therefore, we can't learn much about the treatment from the instrument.\n",
    "\n",
    "The formulas for the IV standard errors are a bit complex and not so intuitive, so we will try something else to grasp this problem. We will simulate data where we have a treatment T with effect 2.0 on the outcome Y, an unobserved confounder U and an additional control X. We will also simulate multiple instruments with different strengths on the 1st stage.\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "X \\sim & N(0, 2^2)\\\\\n",
    "U \\sim & N(0, 2^2)\\\\\n",
    "T \\sim & N(1+0.5U, 5^2)\\\\\n",
    "Y \\sim & N(2+ X - 0.5U + 2T, 5^2)\\\\\n",
    "Z \\sim & N(T, \\sigma^2) \\text{ for }\\sigma^2 \\text{ in 0.1 to 100}\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>U</th>\n",
       "      <th>T</th>\n",
       "      <th>...</th>\n",
       "      <th>Z_48</th>\n",
       "      <th>Z_49</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.696148</td>\n",
       "      <td>8.056988</td>\n",
       "      <td>...</td>\n",
       "      <td>-117.798705</td>\n",
       "      <td>-13.485292</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.570240</td>\n",
       "      <td>0.245067</td>\n",
       "      <td>...</td>\n",
       "      <td>-209.727577</td>\n",
       "      <td>-70.792948</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.664741</td>\n",
       "      <td>5.597510</td>\n",
       "      <td>...</td>\n",
       "      <td>60.562232</td>\n",
       "      <td>47.619414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.037725</td>\n",
       "      <td>0.493532</td>\n",
       "      <td>...</td>\n",
       "      <td>78.136513</td>\n",
       "      <td>-108.322304</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.590591</td>\n",
       "      <td>-6.263014</td>\n",
       "      <td>...</td>\n",
       "      <td>78.776566</td>\n",
       "      <td>-80.547214</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 53 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "          U         T  ...        Z_48        Z_49\n",
       "0  2.696148  8.056988  ... -117.798705  -13.485292\n",
       "1  2.570240  0.245067  ... -209.727577  -70.792948\n",
       "2  0.664741  5.597510  ...   60.562232   47.619414\n",
       "3  1.037725  0.493532  ...   78.136513 -108.322304\n",
       "4 -2.590591 -6.263014  ...   78.776566  -80.547214\n",
       "\n",
       "[5 rows x 53 columns]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(12)\n",
    "n = 10000\n",
    "X = np.random.normal(0, 2, n) # observable variable\n",
    "U = np.random.normal(0, 2, n) # unobservable (omitted) variable\n",
    "T = np.random.normal(1 + 0.5*U, 5, n) # treatment\n",
    "Y = np.random.normal(2 + X - 0.5*U + 2*T, 5, n) # outcome\n",
    "\n",
    "stddevs = np.linspace(0.1, 100, 50)\n",
    "Zs = {f\"Z_{z}\": np.random.normal(T, s, n) for z, s in enumerate(stddevs)} # instruments with decreasing \\mathrm{Cov}(Z, T)\n",
    "\n",
    "sim_data = pd.DataFrame(dict(U=U, T=T, Y=Y)).assign(**Zs)\n",
    "\n",
    "sim_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just to double check, we can see that the correlation between Z and T is indeed decreasing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Z_0    0.999807\n",
       "Z_1    0.919713\n",
       "Z_2    0.773434\n",
       "Z_3    0.634614\n",
       "Z_4    0.523719\n",
       "Name: T, dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corr = (sim_data.corr()[\"T\"]\n",
    "        [lambda d: d.index.str.startswith(\"Z\")])\n",
    "\n",
    "corr.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will run one IV model per instrument we have and collect both the ATE estimate and the standard error."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "se = []\n",
    "ate = []\n",
    "for z in range(len(Zs)):\n",
    "    formula = f'Y ~ 1 + X + [T ~ Z_{z}]'\n",
    "    iv = IV2SLS.from_formula(formula, sim_data).fit()\n",
    "    se.append(iv.std_errors[\"T\"])\n",
    "    ate.append(iv.params[\"T\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data = pd.DataFrame(dict(se=se, ate=ate, corr=corr)).sort_values(by=\"corr\")\n",
    "\n",
    "plt.scatter(plot_data[\"corr\"], plot_data[\"se\"])\n",
    "plt.xlabel(\"Corr(Z, T)\")\n",
    "plt.ylabel(\"IV Standard Error\");\n",
    "plt.title(\"Variance of the IV Estimates by 1st Stage Strength\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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    "plt.scatter(plot_data[\"corr\"], plot_data[\"ate\"])\n",
    "plt.fill_between(plot_data[\"corr\"],\n",
    "                 plot_data[\"ate\"]+1.96*plot_data[\"se\"],\n",
    "                 plot_data[\"ate\"]-1.96*plot_data[\"se\"], alpha=.5)\n",
    "plt.xlabel(\"Corr(Z, T)\")\n",
    "plt.ylabel(\"$\\hat{ATE}$\");\n",
    "plt.title(\"IV ATE Estimates by 1st Stage Strength\");"
   ]
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    "As we can see in the plots above, estimates vary wildly when the correlation between T and Z is weak. This is because the SE also increases a lot when the correlation is low.\n",
    "\n",
    "Another thing to notice is that **2SLS is biased**! Even with high correlation, the parameter estimate still does not reach the true ATE of 2.0. Actually, 2.0 is not even in the 95% CI! 2SLS is only consistent, which means that it approaches the true parameter value if the sample size is big enough. However, we can't know how big is big enough. We can only stick to some rules of thumb to understand how this bias behaves:\n",
    "\n",
    "1. 2SLS is biased towards OLS. This means that if OLS has a negative/positive bias, 2SLS will also have it. The advantage of 2SLS is that it is at least consistent, where OLS is not, in the case of omitted variables. In the example above, our unobserved U impacts negatively the outcome but its positively correlated with the treatment, which will result in a negative bias. That is why we are seeing the ATE estimate below the true value (negative bias).\n",
    "\n",
    "2. The bias will increase with the number of instruments we add. If we add too many instruments, 2SLS becomes more and more like OLS.\n",
    "\n",
    "Besides knowing how this bias behaves, a final piece of advice is to avoid some **common mistakes when doing IV**:\n",
    "\n",
    "1. Doing IV by hand. As we've seen, IV by hand will result in wrong standard errors, even if the parameter estimates are right. The SE won't be completely off. Still, why do it if you can use software and get the right SE?\n",
    "\n",
    "2. Using anything other than OLS on the 1st stage. Lots of Data Scientist encounter IV and think they can do better. For example, they see a dummy treatment and think about replacing the 1st stage by a logistic regression, after all, they are predicting a dummy variable, right?. The problem is that this is plain wrong. The consistency of IV relies on a property that only OLS can give, which is the orthogonality of the residuals, so anything different than OLS on the 1st stage will yield something biased. (OBS: there are some modern techniques that use Machine Learning for IV, but their results have been, at best, questionable).\n",
    "\n",
    "## Key Ideas\n",
    "\n",
    "We've taken some time here to understand how we can work around omitted variable bias if we have an instrument variable. An instrument is a variable that is correlated with the treatment (has a first stage), but only affects the outcome through the treatment (exclusion restriction). We saw an example of an instrument with quarter of birth to estimate the effect of education on income.\n",
    "\n",
    "We then delve into the mechanics of estimating the causal effect with IV, namely, using 2SLS. We've also learned that IV is no silver bullet. It can be quite troublesome when we have a weak first stage. Also, although consistent, 2SLS is still a biased method to estimate the causal effect. \n",
    "\n",
    "## References\n",
    "\n",
    "I like to think of this entire book as a tribute to Joshua Angrist, Alberto Abadie and Christopher Walters for their amazing Econometrics class. Most of the ideas here are taken from their classes at the American Economic Association. Watching them is what is keeping me sane during this tough year of 2020.\n",
    "* [Cross-Section Econometrics](https://www.aeaweb.org/conference/cont-ed/2017-webcasts)\n",
    "* [Mastering Mostly Harmless Econometrics](https://www.aeaweb.org/conference/cont-ed/2020-webcasts)\n",
    "\n",
    "I'll also like to reference the amazing books from Angrist. They have shown me that Econometrics, or 'Metrics as they call it, is not only extremely useful but also profoundly fun.\n",
    "\n",
    "* [Mostly Harmless Econometrics](https://www.mostlyharmlesseconometrics.com/)\n",
    "* [Mastering 'Metrics](https://www.masteringmetrics.com/)\n",
    "\n",
    "My final reference is Miguel Hernan and Jamie Robins' book. It has been my trustworthy companion in the most thorny causal questions I had to answer.\n",
    "\n",
    "* [Causal Inference Book](https://www.hsph.harvard.edu/miguel-hernan/causal-inference-book/)\n",
    "\n",
    "![img](./data/img/poetry.png)\n",
    "\n",
    "## Contribute\n",
    "\n",
    "Causal Inference for the Brave and True is an open-source material on causal inference, the statistics of science. It uses only free software, based in Python. Its goal is to be accessible monetarily and intellectually.\n",
    "If you found this book valuable and you want to support it, please go to [Patreon](https://www.patreon.com/causal_inference_for_the_brave_and_true). If you are not ready to contribute financially, you can also help by fixing typos, suggesting edits or giving feedback on passages you didn't understand. Just go to the book's repository and [open an issue](https://github.com/matheusfacure/python-causality-handbook/issues). Finally, if you liked this content, please share it with others who might find it useful and give it a [star on GitHub](https://github.com/matheusfacure/python-causality-handbook/stargazers)."
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